From 86c7801143d0c3a6221e8cc66b41d8c02ff6b5b1 Mon Sep 17 00:00:00 2001 From: kevin sheppard Date: Mon, 26 Mar 2012 10:04:23 +0100 Subject: [PATCH] Initial import --- Contents.m | 2 + GUI/ARMAX.fig | Bin 0 -> 10766 bytes GUI/ARMAX.m | 1282 +++++++++++++++++ GUI/ARMAX_about.fig | Bin 0 -> 7011 bytes GUI/ARMAX_about.m | 206 +++ GUI/ARMAX_close_dialog.fig | Bin 0 -> 6687 bytes GUI/ARMAX_close_dialog.m | 207 +++ GUI/ARMAX_viewer.fig | Bin 0 -> 8388 bytes GUI/ARMAX_viewer.m | 800 ++++++++++ GUI/OxLogo.mat | Bin 0 -> 12247 bytes addToPath.m | 73 + bootstrap/block_bootstrap.m | 77 + bootstrap/bsds.m | 176 +++ bootstrap/mcs.m | 190 +++ bootstrap/robustvcv.m | 82 ++ bootstrap/stationary_bootstrap.m | 69 + crosssection/ols.m | 128 ++ crosssection/pca.m | 118 ++ distributions/gedcdf.m | 71 + distributions/gedinv.m | 90 ++ distributions/gedloglik.m | 74 + distributions/gedpdf.m | 56 + distributions/gedrnd.m | 64 + distributions/mvnormloglik.m | 102 ++ distributions/normloglik.m | 74 + distributions/skewtcdf.m | 59 + distributions/skewtinv.m | 55 + distributions/skewtloglik.m | 86 ++ distributions/skewtpdf.m | 50 + distributions/skewtrnd.m | 51 + distributions/stdtcdf.m | 42 + distributions/stdtinv.m | 42 + distributions/stdtloglik.m | 70 + distributions/stdtpdf.m | 45 + distributions/stdtrnd.m | 51 + dlls/agarch_core.mexw64 | Bin 0 -> 9728 bytes dlls/armaxerrors.mexw64 | Bin 0 -> 9216 bytes dlls/egarch_core.mexw64 | Bin 0 -> 9728 bytes dlls/igarch_core.mexw64 | Bin 0 -> 9216 bytes dlls/tarch_core.mexw64 | Bin 0 -> 9216 bytes duplication/chi2cdf.m | 39 + duplication/iscompatible.m | 145 ++ duplication/kurtosis.m | 27 + duplication/normcdf.m | 49 + duplication/norminv.m | 49 + duplication/normpdf.m | 51 + duplication/skewness.m | 27 + mex_source/agarch_core.c | 105 ++ mex_source/armaxerrors.c | 110 ++ mex_source/egarch_core.c | 120 ++ mex_source/igarch_core.c | 84 ++ mex_source/tarch_core.c | 85 ++ multivariate/ccc_mvgarch.m | 242 ++++ multivariate/ccc_mvgarch_joint_likelihood.m | 76 + multivariate/ccc_mvgarch_likelihood.m | 36 + multivariate/ccc_mvgarch_simulate.m | 167 +++ multivariate/matrix_garch.m | 259 ++++ multivariate/matrix_garch_display.m | 91 ++ multivariate/matrix_garch_likelihood.m | 87 ++ multivariate/matrix_garch_simulate.m | 198 +++ multivariate/o_mvgarch.m | 180 +++ multivariate/riskmetrics.m | 81 ++ multivariate/riskmetrics2006.m | 171 +++ multivariate/scalar_vt_vech.m | 267 ++++ multivariate/scalar_vt_vech_itransform.m | 49 + multivariate/scalar_vt_vech_jointlikelihood.m | 82 ++ multivariate/scalar_vt_vech_likelihood.m | 105 ++ multivariate/scalar_vt_vech_simulate.m | 154 ++ multivariate/scalar_vt_vech_starting_values.m | 75 + multivariate/scalar_vt_vech_transform.m | 76 + realized/ES_20090817.mat | Bin 0 -> 2084778 bytes realized/Since the changed in QRV - 2.docx | Bin 0 -> 22608 bytes realized/Since the changed in QRV.docx | Bin 0 -> 21075 bytes realized/ToDo.docx | Bin 0 -> 13117 bytes realized/realized_bipower_variation.m | 196 +++ realized/realized_compute_median.m | 122 ++ realized/realized_convert2unit.m | 133 ++ realized/realized_covariance.m | 216 +++ realized/realized_hayashi_yoshida.m | 311 ++++ realized/realized_kernel.m | 415 ++++++ realized/realized_kernel_bandwidth.m | 126 ++ realized/realized_kernel_core.m | 115 ++ realized/realized_kernel_jitter_lag_length.m | 202 +++ realized/realized_kernel_weights.m | 124 ++ realized/realized_min_med_variance.m | 191 +++ realized/realized_multiscale_variance.m | 374 +++++ realized/realized_multivariate_kernel.m | 495 +++++++ realized/realized_noise_estimate.m | 121 ++ realized/realized_options.m | 207 +++ realized/realized_price_filter.m | 281 ++++ realized/realized_qmle_variance.m | 233 +++ realized/realized_quantile_scales.mat | Bin 0 -> 549815 bytes realized/realized_quantile_variance.m | 360 +++++ realized/realized_quantile_variance_scale.m | 97 ++ .../realized_quantile_weight_simulation.m | 95 ++ realized/realized_quarticity.m | 235 +++ realized/realized_range.m | 276 ++++ realized/realized_range_simulation.m | 59 + .../realized_range_simulation_results.mat | Bin 0 -> 1616 bytes realized/realized_refresh_time.m | 120 ++ realized/realized_refresh_time_bivariate.m | 98 ++ realized/realized_return_filter.m | 196 +++ realized/realized_semivariance.m | 163 +++ realized/realized_subsample.m | 149 ++ realized/realized_test.m | 92 ++ .../realized_threshold_multipower_variation.m | 49 + realized/realized_threshold_variance.m | 277 ++++ realized/realized_twoscale_variance.m | 352 +++++ realized/realized_variance.m | 157 ++ realized/realized_variance_optimal_sampling.m | 359 +++++ realized/seconds2unit.m | 65 + realized/seconds2wall.m | 42 + realized/unit2seconds.m | 63 + realized/unit2wall.m | 66 + realized/wall2seconds.m | 49 + realized/wall2unit.m | 77 + tests/berkowitz.m | 129 ++ tests/jarquebera.m | 73 + tests/kolmogorov.m | 232 +++ tests/ljungbox.m | 61 + tests/lmtest1.m | 82 ++ timeseries/acf.m | 126 ++ timeseries/aichqcsbic.m | 125 ++ timeseries/aicsbic.m | 125 ++ timeseries/arma_forecaster.m | 254 ++++ timeseries/armaroots.m | 129 ++ timeseries/armaxerrors.m | 50 + timeseries/armaxfilter.m | 452 ++++++ timeseries/armaxfilter_core.m | 36 + timeseries/armaxfilter_likelihood.m | 57 + timeseries/armaxfilter_simulate.m | 174 +++ timeseries/augdf.m | 148 ++ timeseries/augdf_cvsim_tieup.m | 49 + timeseries/augdfautolag.m | 155 ++ timeseries/augdfcv.m | 418 ++++++ timeseries/beveridgenelson.m | 156 ++ timeseries/bkfilter.m | 104 ++ timeseries/convert_ma_roots.m | 33 + timeseries/grangercause.m | 358 +++++ timeseries/heterogeneousar.m | 253 ++++ timeseries/hp_filter.m | 87 ++ timeseries/impulseresponse.m | 376 +++++ timeseries/impulseresponse_bootstrap.m | 379 +++++ timeseries/inverse_ar_roots.m | 35 + timeseries/olsnw.m | 132 ++ timeseries/pacf.m | 90 ++ timeseries/sacf.m | 121 ++ timeseries/spacf.m | 114 ++ timeseries/tsresidualplot.m | 142 ++ timeseries/vectorar.m | 212 +++ timeseries/vectorarvcv.m | 66 + univariate/agarch.m | 190 +++ univariate/agarch_core.m | 82 ++ univariate/agarch_display.m | 245 ++++ univariate/agarch_itransform.m | 121 ++ univariate/agarch_likelihood.m | 85 ++ univariate/agarch_parameter_check.m | 177 +++ univariate/agarch_simulate.m | 175 +++ univariate/agarch_starting_values.m | 87 ++ univariate/agarch_transform.m | 134 ++ univariate/aparch.m | 246 ++++ univariate/aparch_core.m | 71 + univariate/aparch_display.m | 263 ++++ univariate/aparch_itransform.m | 120 ++ univariate/aparch_likelihood.m | 109 ++ univariate/aparch_loglikelihood.m | 0 univariate/aparch_parameter_check.m | 178 +++ univariate/aparch_simulate.m | 196 +++ univariate/aparch_starting_values.m | 84 ++ univariate/aparch_transform.m | 148 ++ univariate/egarch.m | 253 ++++ univariate/egarch_core.m | 90 ++ univariate/egarch_display.m | 232 +++ univariate/egarch_itransform.m | 57 + univariate/egarch_likelihood.m | 92 ++ univariate/egarch_nlcon.m | 29 + univariate/egarch_parameter_check.m | 150 ++ univariate/egarch_simulate.m | 163 +++ univariate/egarch_starting_values.m | 127 ++ univariate/egarch_transform.m | 60 + univariate/figarch.m | 233 +++ univariate/figarch_itransform.m | 101 ++ univariate/figarch_likelihood.m | 72 + univariate/figarch_parameter_check.m | 178 +++ univariate/figarch_simulate.m | 196 +++ univariate/figarch_starting_values.m | 126 ++ univariate/figarch_transform.m | 94 ++ univariate/figarch_weights.m | 61 + univariate/igarch.m | 268 ++++ univariate/igarch_core.m | 76 + univariate/igarch_display.m | 271 ++++ univariate/igarch_itransform.m | 111 ++ univariate/igarch_likelihood.m | 87 ++ univariate/igarch_parameter_check.m | 168 +++ univariate/igarch_starting_values.m | 130 ++ univariate/igarch_transform.m | 136 ++ univariate/tarch.m | 274 ++++ univariate/tarch_core.m | 77 + univariate/tarch_display.m | 265 ++++ univariate/tarch_itransform.m | 122 ++ univariate/tarch_likelihood.m | 85 ++ univariate/tarch_parameter_check.m | 168 +++ univariate/tarch_simulate.m | 171 +++ univariate/tarch_starting_values.m | 154 ++ univariate/tarch_transform.m | 174 +++ utility/c2mdate.m | 60 + utility/chol2vec.m | 39 + utility/corr_ivech.m | 51 + utility/corr_vech.m | 39 + utility/cov2corr.m | 15 + utility/covnw.m | 78 + utility/covvar.m | 184 +++ utility/demean.m | 23 + utility/dirod.m | 48 + utility/gradient_2sided.m | 74 + utility/hessian_2sided.m | 81 ++ utility/hessian_2sided_nrows.m | 85 ++ utility/ivech.m | 56 + utility/m2cdate.m | 55 + utility/mprint.m | 298 ++++ utility/mvstandardize.m | 72 + utility/newlagmatrix.m | 78 + utility/pltdens.m | 85 ++ utility/randchar.m | 5 + utility/standardize.m | 45 + utility/vec2chol.m | 54 + utility/vech.m | 38 + utility/x2mdate.m | 79 + 228 files changed, 30074 insertions(+) create mode 100644 Contents.m create mode 100644 GUI/ARMAX.fig create mode 100644 GUI/ARMAX.m create mode 100644 GUI/ARMAX_about.fig create mode 100644 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z36D>?L8J8od-(nK(9AoOslcQ5ElZr?FG+yN73J<^ujdQ=LNzWz&AD~$uWVWurlI5a z+fjq|?2}Xwrrt!}btf?Qt^iWG7e_&M@n-@V zS%SNCBg-HnbLP#x1-Q2iq#CYRQ)I^EgOk)WnEB|BhlX#c%a+z=F^skAo~|icPv~bY5__#dJzfudsMoX7{|`^rxfuWe literal 0 HcmV?d00001 diff --git a/GUI/ARMAX.m b/GUI/ARMAX.m new file mode 100644 index 0000000..510fdf4 --- /dev/null +++ b/GUI/ARMAX.m @@ -0,0 +1,1282 @@ +function varargout = ARMAX(varargin) +% ARMAX M-file for ARMAX.fig +% ARMAX, by itself, creates a new ARMAX or raises the existing +% singleton*. +% +% H = ARMAX returns the handle to a new ARMAX or the handle to +% the existing singleton*. +% +% ARMAX('CALLBACK',hObject,eventData,handles,...) calls the local +% function named CALLBACK in ARMAX.M with the given input arguments. +% +% ARMAX('Property','Value',...) creates a new ARMAX or raises the +% existing singleton*. Starting from the left, property value pairs are +% applied to the GUI before ARMAX_OpeningFunction gets called. An +% unrecognized property name or invalid value makes property application +% stop. All inputs are passed to ARMAX_OpeningFcn via varargin. +% +% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one +% instance to run (singleton)". +% +% See also: GUIDE, GUIDATA, GUIHANDLES + +% Edit the above text to modify the response to help ARMAX + +% Last Modified by GUIDE v2.5 29-Jan-2007 16:09:05 + +% Begin initialization code - DO NOT EDIT +gui_Singleton = 1; +gui_State = struct('gui_Name', mfilename, ... + 'gui_Singleton', gui_Singleton, ... + 'gui_OpeningFcn', @ARMAX_OpeningFcn, ... + 'gui_OutputFcn', @ARMAX_OutputFcn, ... + 'gui_LayoutFcn', [] , ... + 'gui_Callback', []); +if nargin && ischar(varargin{1}) + gui_State.gui_Callback = str2func(varargin{1}); +end + +if nargout + [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); +else + gui_mainfcn(gui_State, varargin{:}); +end +% End initialization code - DO NOT EDIT + + +% --- Executes just before ARMAX is made visible. +function ARMAX_OpeningFcn(hObject, eventdata, handles, varargin) +% This function has no output args, see OutputFcn. +% hObject handle to figure +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +% varargin command line arguments to ARMAX (see VARARGIN) + +% Choose default command line output for ARMAX +handles.output = hObject; + +handles.model_ARMAX_AR_order=[]; +handles.model_ARMAX_MA_order=[]; +handles.model_ARMAX_AR_order_string=''; +handles.model_ARMAX_MA_order_string=''; +handles.y = varargin{1}; +handles.model_ARMAX_residuals=[]; +handles.ACF_lags=min(24,floor(length(handles.y)/8)); +handles.model_InferenceMethod = 1; +handles.model_IncludeConstant=1; +handles.models={}; +% Update handles structure +guidata(hObject, handles); +% UIWAIT makes ARMAX wait for user response (see UIRESUME) +% uiwait(handles.figure1); + +axes(handles.plot_handle); +clear_axes(handles) +h=plot(handles.y); +set(h,'LineWidth',2,'Color',[0 0 .6]) +axis tight; +title('Plot of original data') +AX=axis; +range = AX(4)-AX(3); +AX(3)=AX(3)-.1*range; +AX(4)=AX(4)+.1*range; +axis(AX); + +set(handles.heterorobust_menu,'Checked','on') +set(handles.homoerror_menu,'Checked','off') +set(handles.ACF_lags_edit,'String',num2str(handles.ACF_lags)) + +% --- Outputs from this function are returned to the command line. +function varargout = ARMAX_OutputFcn(hObject, eventdata, handles) +% varargout cell array for returning output args (see VARARGOUT); +% hObject handle to figure +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Get default command line output from handles structure +varargout{1} = handles.output; + + +% --- Executes on button press in pushbutton1. +function pushbutton1_Callback(hObject, eventdata, handles) +% hObject handle to pushbutton1 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + + + +function EXOG_edit_Callback(hObject, eventdata, handles) +% hObject handle to EXOG_edit (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hints: get(hObject,'String') returns contents of EXOG_edit as text +% str2double(get(hObject,'String')) returns contents of EXOG_edit as a double + + +% --- Executes during object creation, after setting all properties. +function EXOG_edit_CreateFcn(hObject, eventdata, handles) +% hObject handle to EXOG_edit (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles empty - handles not created until after all CreateFcns called + +% Hint: edit controls usually have a white background on Windows. +% See ISPC and COMPUTER. +if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) + set(hObject,'BackgroundColor','white'); +end + +% --- Executes on button press in pushbutton2. +function pushbutton2_Callback(hObject, eventdata, handles) +% hObject handle to pushbutton2 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + + + +function edit2_Callback(hObject, eventdata, handles) +% hObject handle to edit2 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hints: get(hObject,'String') returns contents of edit2 as text +% str2double(get(hObject,'String')) returns contents of edit2 as a double + + +% --- Executes during object creation, after setting all properties. +function edit2_CreateFcn(hObject, eventdata, handles) +% hObject handle to edit2 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles empty - handles not created until after all CreateFcns called + +% Hint: edit controls usually have a white background on Windows. +% See ISPC and COMPUTER. +if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) + set(hObject,'BackgroundColor','white'); +end + + + +% --- Executes on button press in estimate_pushbutton. +function estimate_pushbutton_Callback(hObject, eventdata, handles) +% hObject handle to estimate_pushbutton (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +%Thsi is the main function. Call ARMACFILTER and then call teh display +%routine to display the results. Make sure there are no errorr, if there +%are display a message that something went wrrong. +y=handles.y; +ar = handles.model_ARMAX_AR_order; +ma = handles.model_ARMAX_MA_order; +constant = handles.model_IncludeConstant; + +% A couple of quick sanity checks +readytorun = true; +notalreadyrun = true; +if (isempty(ar) || all(ar==0)) && (isempty(ma) || all(ma==0)) + readytorun=false; +end + +% Check to make sure the this model hasn't been estimated; if it has, +% do not reestimate but load the results of the previous estimation. +% Probably print a message in th3 window. + +% To check, compare teh constant, and the other things, if a match is +% founf, set readyto run to false, update a message and display the model +% results by changing the current model number. + + + +models = handles.models; +matchedModel=0; +for i=1:length(handles.models) + match=true; + thisModel = models{i}; + % conditions for maths + % constant == modelcontant + % length(ar)==length(modelar) + % if true than check that they are all the same + % length(ma)==length(modelma) + % if true than check that they are all the same + + if constant ~= thisModel.constant + match=false; + end + + if length(ar)~=length(thisModel.ARlags) + match=false; + elseif ~all(unique(ar)==unique(thisModel.ARlags)) + match=false; + end + + if length(ma)~=length(thisModel.MAlags) + match=false; + elseif ~all(unique(ma)==unique(thisModel.MAlags)) + match=false; + end + + if match + matchedModel=i; + notalreadyrun = false; + end +end + +if matchedModel + handles.currentModelNumber = matchedModel; + errors = models{matchedModel}.errors; +end + + + + + +if readytorun && notalreadyrun + try + [parameters, ll, errors, seregression, diagnostics, vcvrobust, vcv, likelihoods, scores]=armaxfilter(y,constant,ar,ma); + handles.model_ARMAX_residuals=errors; + modelno=length(handles.models)+1; + handles.models{modelno}.parameters=parameters; + handles.models{modelno}.errors=errors; + handles.models{modelno}.ll=ll; + handles.models{modelno}.seregression=seregression; + handles.models{modelno}.diagnostics=diagnostics; + if handles.model_InferenceMethod + handles.models{modelno}.covariance=vcvrobust; + else + handles.models{modelno}.covariance=vcv; + end + handles.models{modelno}.likelihoods=likelihoods; + handles.models{modelno}.scores=scores; + handles.models{modelno}.ARlags=ar; + handles.models{modelno}.MAlags=ma; + handles.models{modelno}.constant=constant; + handles.models{modelno}.y=y; + handles.models{modelno}.yhat=y-errors; + [aic,bic]=aicsbic(errors,constant,ar,ma); + handles.models{modelno}.AIC=aic; + handles.models{modelno}.BIC=bic; + handles.models{modelno}.K=length(parameters); + handles.models{modelno}.StdErr=sqrt(diag(handles.models{modelno}.covariance)); + handles.models{modelno}.Tstat=parameters./handles.models{modelno}.StdErr; + handles.models{modelno}.Pval=2-2*normcdf(abs(handles.models{modelno}.Tstat)); + + % Update the string in the popup + ar = handles.models{modelno}.ARlags; + ma = handles.models{modelno}.MAlags; + irregular = false; + if ~isempty(ar) + if length(ar)UB; + val = UB; +elseif floor(val)~=val + val=floor(val); +else + OK = true; +end + + + + +% -------------------------------------------------------------------- +function about_menu_Callback(hObject, eventdata, handles) +% hObject handle to about_menu (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +value = ARMAX_about('Title','About'); + + + +function no_model_run_plot(ax,handles) +axes(ax); +clear_axes(handles) +h=plot([0 1],[0 1]); +axis tight +set(h,'Visible','off') +t=text(.1,.5,'You must estimate a model before residual plots can be produced'); +set(t,'FontWeight','bold','FontSize',8,'FontName','Tahoma') +set(get(h,'Parent'),'XTick',[],'YTick',[],'XColor',[1 1 1],'YColor',[1 1 1]) + + +% -------------------------------------------------------------------- +function stderror_menu_Callback(hObject, eventdata, handles) +% hObject handle to stderror_menu (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + + +% -------------------------------------------------------------------- +function heterorobust_menu_Callback(hObject, eventdata, handles) +% hObject handle to heterorobust_menu (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +handles.model_InferenceMethod = 1; +set(hObject,'Checked','on') +set(handles.homoerror_menu,'Checked','off') +guidata(hObject, handles); +set(handles.message_text,'String',['Inference will be made using a heteroskedasticity robust covariace estimator.'],'ForegroundColor',[0 0 0]) + + + + + +% -------------------------------------------------------------------- +function homoerror_menu_Callback(hObject, eventdata, handles) +% hObject handle to homoerror_menu (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +handles.model_InferenceMethod = 0; +set(hObject,'Checked','on') +set(handles.heterorobust_menu,'Checked','off') +guidata(hObject, handles); +set(handles.message_text,'String',['Inference will be made assuming homoskedastic errors.'],'ForegroundColor',[0 0 0]) + + + + +function [lags, str, OK] = validate_AR_MA_lags(str,old_lags,old_str) +% This code will do the input validation for the strings used for the AR +% and MA lags + +% Lags must be less than T-1 +% Must be > 0 + +% first things to do is to find the spaces. From here I can break up the +% string into units which have to be of one type, either a number (#) or a +% number-colon-number combo (#:#). Any failure and the OK = 0 and the +% program should terminate. + +if isempty(str) || all(ismember(str',' ')) + OK = true; + lags = []; + str = ''; + return +end + +% The fisr check is to verify that all the elements are in {1,2,...,9,0,:} + +valid=all(ismember(str',{'1','2','3','4','5','6','7','8','9','0',':',' '})); +lags=[]; +OK = false; +if valid + try + eval(['lags=[' str '];']); + catch + OK = false; + end +end +if ~isempty(lags) + lags = unique(lags); + OK=true; +else + str = old_str; + OK = false; +end + + + + + + +% --- Executes on selection change in model_selector_popup. +function model_selector_popup_Callback(hObject, eventdata, handles) +% hObject handle to model_selector_popup (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hints: contents = get(hObject,'String') returns model_selector_popup contents as cell array +% contents{get(hObject,'Value')} returns selected item from model_selector_popup + +% 1. Update AR Lags, MA Lags and Constant +model = handles.models{get(hObject,'Value')}; +set(handles.AR_lags_edit,'String',num2str(model.ARlags)) +set(handles.MA_lags_edit,'String',num2str(model.MAlags)) +% 2. Change residuals +handles.model_ARMAX_residuals=model.errors; +% 3. Graph raw residuals +y=handles.model_ARMAX_residuals; +axes(handles.plot_handle); +clear_axes(handles) +hold off; +% Need to produce a plot +h=plot(y); +set(h,'LineWidth',2,'Color',[0 0 .6]) +axis tight; +title('Plot of estimated errors') +AX=axis; +range = AX(4)-AX(3); +AX(3)=AX(3)-.1*range; +AX(4)=AX(4)+.1*range; +axis(AX); +% 4. Change Radio button +set(handles.resid_raw_radio,'Value',1) +% 2. Update Message +set(handles.message_text,'String',['Results from model ' model.StringID ' loaded.'],'ForegroundColor',[0 0 .9]) + + +% --- Executes during object creation, after setting all properties. +function model_selector_popup_CreateFcn(hObject, eventdata, handles) +% hObject handle to model_selector_popup (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles empty - handles not created until after all CreateFcns called + +% Hint: popupmenu controls usually have a white background on Windows. +% See ISPC and COMPUTER. +if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) + set(hObject,'BackgroundColor','white'); +end + + +% --- Executes during object creation, after setting all properties. +function constant_include_CreateFcn(hObject, eventdata, handles) +% hObject handle to constant_include (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles empty - handles not created until after all CreateFcns called + + +% --- Executes on button press in constant_include. +function constant_include_Callback(hObject, eventdata, handles) +% hObject handle to constant_include (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of constant_include +handles.model_IncludeConstant=1; +guidata(hObject, handles); +set(handles.message_text,'String','Model will include a constant.','ForegroundColor',[0 0 0]) + + + +% --- Executes on button press in constant_exclude. +function constant_exclude_Callback(hObject, eventdata, handles) +% hObject handle to constant_exclude (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of constant_exclude +handles.model_IncludeConstant=0; +guidata(hObject, handles); +set(handles.message_text,'String','Model will not include a constant.','ForegroundColor',[0 0 0]) + + + + +% --- Executes on button press in orig_raw_radio. +function orig_raw_radio_Callback(hObject, eventdata, handles) +% hObject handle to orig_raw_radio (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of orig_raw_radio +y=handles.y; +axes(handles.plot_handle); +clear_axes(handles) +hold off; +% Need to produce a plot +h=plot(y); +set(h,'LineWidth',2,'Color',[0 0 .6]) +axis tight; +title('Plot of original data') +AX=axis; +range = AX(4)-AX(3); +AX(3)=AX(3)-.1*range; +AX(4)=AX(4)+.1*range; +axis(AX); + + + + +% --- Executes on button press in orig_acf_radio. +function orig_acf_radio_Callback(hObject, eventdata, handles) +% hObject handle to orig_acf_radio (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of orig_acf_radio + +y=handles.y; +ACF_lags=handles.ACF_lags; +robust=handles.model_InferenceMethod; +axes(handles.plot_handle); +clear_axes(handles); +hold off; +[ac,acstd]=sacf(y,ACF_lags,robust,0); + +h = bar(ac); +set(h,'FaceColor',[.5 .5 1]); +axis tight; +ax = axis; +spread = .2*(ax(4)-ax(3)); +ax(1) = 0; +ax(2) = ACF_lags+1; +ax(3) = ax(3) - spread; +ax(4) = ax(4) + spread; +axis(ax); +hold on; +h2 = plot((0:ACF_lags+1)',[[acstd(1);acstd;acstd(ACF_lags)] -[acstd(1);acstd;acstd(ACF_lags)]]); + +if robust + title('Sample Autocorrelations and Robust Standard Errors'); +else + title('Sample Autocorrelations and Non-robust Standard Errors'); +end + +set(h2(1),'LineWidth',2,'LineStyle',':','Color',[0 0 0]); +set(h2(2),'LineWidth',2,'LineStyle',':','Color',[0 0 0]); + + +% --- Executes on button press in orig_pacf_radio. +function orig_pacf_radio_Callback(hObject, eventdata, handles) +% hObject handle to orig_pacf_radio (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of orig_pacf_radio +y=handles.y; +ACF_lags=handles.ACF_lags; +robust=handles.model_InferenceMethod; +axes(handles.plot_handle); +clear_axes(handles) +hold off; +[pac,pacstd]=spacf(y,ACF_lags,robust,0); + +h = bar(pac); +set(h,'FaceColor',[.5 .5 1]); +axis tight; +ax = axis; +spread = .2*(ax(4)-ax(3)); +ax(1) = 0; +ax(2) = ACF_lags+1; +ax(3) = ax(3) - spread; +ax(4) = ax(4) + spread; +axis(ax); +hold on; +h2 = plot((0:ACF_lags+1)',[2*[pacstd(1);pacstd;pacstd(ACF_lags)] -2*[pacstd(1);pacstd;pacstd(ACF_lags)]]); + +if robust + title('Sample Partial Autocorrelations and Robust Standard Errors'); +else + title('Sample Partial Autocorrelations and Non-robust Standard Errors'); +end + +set(h2(1),'LineWidth',2,'LineStyle',':','Color',[0 0 0]); +set(h2(2),'LineWidth',2,'LineStyle',':','Color',[0 0 0]); + + + +% --- Executes on button press in resid_raw_radio. +function resid_raw_radio_Callback(hObject, eventdata, handles) +% hObject handle to resid_raw_radio (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of resid_raw_radio + +if isempty(handles.model_ARMAX_residuals) + no_model_run_plot(handles.plot_handle,handles); +else + y=handles.model_ARMAX_residuals; + axes(handles.plot_handle); + clear_axes(handles) + hold off; + % Need to produce a plot + h=plot(y); + set(h,'LineWidth',2,'Color',[0 0 .6]) + axis tight; + title('Plot of estimated errors') + AX=axis; + range = AX(4)-AX(3); + AX(3)=AX(3)-.1*range; + AX(4)=AX(4)+.1*range; + axis(AX); +end + + + +% --- Executes on button press in resid_fit_radio. +function resid_fit_radio_Callback(hObject, eventdata, handles) +% hObject handle to resid_fit_radio (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of resid_fit_radio +if isempty(handles.model_ARMAX_residuals) + no_model_run_plot(handles.plot_handle,handles); +else + yhat=handles.y-handles.model_ARMAX_residuals; + y=handles.y; + axes(handles.plot_handle); + clear_axes(handles) + hold off; + % Need to produce a plot + h=plot([y yhat]); + set(h(1),'LineWidth',2,'Color',[0 0 .6]) + set(h(2),'LineWidth',2,'Color',[.16 .38 .27]) + axis tight; + title('Plot of estimated errors') + legend('Original Data','Fit Data') + AX=axis; + range = AX(4)-AX(3); + AX(3)=AX(3)-.1*range; + AX(4)=AX(4)+.1*range; + axis(AX); +end + + + + +% --- Executes on button press in resid_acf_radio. +function resid_acf_radio_Callback(hObject, eventdata, handles) +% hObject handle to resid_acf_radio (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of resid_acf_radio + +if isempty(handles.model_ARMAX_residuals) + no_model_run_plot(handles.plot_handle,handles); +else + y=handles.model_ARMAX_residuals; + ACF_lags=handles.ACF_lags; + robust=handles.model_InferenceMethod; + axes(handles.plot_handle); + clear_axes(handles); + hold off; + [ac,acstd]=sacf(y,ACF_lags,robust,0); + + h = bar(ac); + set(h,'FaceColor',[.5 .5 1]); + axis tight; + ax = axis; + spread = .2*(ax(4)-ax(3)); + ax(1) = 0; + ax(2) = ACF_lags+1; + ax(3) = ax(3) - spread; + ax(4) = ax(4) + spread; + axis(ax); + hold on; + h2 = plot((0:ACF_lags+1)',[[acstd(1);acstd;acstd(ACF_lags)] -[acstd(1);acstd;acstd(ACF_lags)]]); + + if robust + title('Sample Autocorrelations and Robust Standard Errors'); + else + title('Sample Autocorrelations and Non-robust Standard Errors'); + end + + set(h2(1),'LineWidth',2,'LineStyle',':','Color',[0 0 0]); + set(h2(2),'LineWidth',2,'LineStyle',':','Color',[0 0 0]); +end + + + +% --- Executes on button press in resid_pacf_radio. +function resid_pacf_radio_Callback(hObject, eventdata, handles) +% hObject handle to resid_pacf_radio (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of resid_pacf_radio + +if isempty(handles.model_ARMAX_residuals) + no_model_run_plot(handles.plot_handle,handles); +else + y=handles.model_ARMAX_residuals; + ACF_lags=handles.ACF_lags; + robust=handles.model_InferenceMethod; + axes(handles.plot_handle); + clear_axes(handles) + + hold off; + [pac,pacstd]=spacf(y,ACF_lags,robust,0); + + h = bar(pac); + set(h,'FaceColor',[.5 .5 1]); + axis tight; + ax = axis; + spread = .2*(ax(4)-ax(3)); + ax(1) = 0; + ax(2) = ACF_lags+1; + ax(3) = ax(3) - spread; + ax(4) = ax(4) + spread; + axis(ax); + hold on; + h2 = plot((0:ACF_lags+1)',[2*[pacstd(1);pacstd;pacstd(ACF_lags)] -2*[pacstd(1);pacstd;pacstd(ACF_lags)]]); + + if robust + title('Sample Partial Autocorrelations and Robust Standard Errors'); + else + title('Sample Partial Autocorrelations and Non-robust Standard Errors'); + end + + set(h2(1),'LineWidth',2,'LineStyle',':','Color',[0 0 0]); + set(h2(2),'LineWidth',2,'LineStyle',':','Color',[0 0 0]); + +end + + + +% --- Executes on button press in radiobutton18. +function radiobutton18_Callback(hObject, eventdata, handles) +% hObject handle to radiobutton18 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of radiobutton18 + + +lags = handles.ACF_lags; +y = handles.y; +if handles.model_InferenceMethod + [stat,pval] = lmtest1(y,lags); + titleString = 'LM Test Statistic Values (left) and P-values (right)'; +else + [stat,pval] = ljungbox(y,lags); + titleString = 'Ljung-Box Q Statistics (left) and P-values (right)'; +end + +clear_axes(handles) +% 1. Set up the axes and their limits +barUL = max(stat)*1.1; +plotUL = 1.1; +plotLL = 0; +barLL = -max(stat)*.1; +axes(handles.plot_handle); +ax=gca; +axis([0 lags+1 barLL barUL]) +set(ax,'XTickMode', 'auto','YTickMode', 'auto','Units','pixels','Position',[32 37 585 392]); +axes(handles.plot_axes2); +axis([0 lags+1 -.1 1.1]) +ax=gca; +set(ax,'YTickMode','auto','Units','pixels','Position',[32 37 585 392],'YAxisLocation','right'); + +% 2. Draw teh bar graph and establish it's limits +axes(handles.plot_handle); +hold on; +b = bar(stat); +set(b,'EdgeColor',[1 1 1],'FaceColor',[.5 .5 1]) +set(get(b(1),'BaseLine'),'LineWidth',1,'LineStyle','none') +hold on; +h = plot(max(stat)*pval); +set(h,'LineWidth',1,'LineStyle','none','Color',[0 0 0],'Marker','s','MarkerFaceColor',[0 0 0],'MarkerEdgeColor',[0 0 0]); +legend('Statistic Value','P-value','Location','NorthWest') + +% 3. Labels and titles +title(titleString) + + + + + +% --- Executes on button press in radiobutton19. +function radiobutton19_Callback(hObject, eventdata, handles) +% hObject handle to radiobutton19 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hint: get(hObject,'Value') returns toggle state of radiobutton19 +if isempty(handles.model_ARMAX_residuals) + no_model_run_plot(handles.plot_handle,handles); +else + lags = handles.ACF_lags; + y=handles.model_ARMAX_residuals; + if handles.model_InferenceMethod + [stat,pval] = lmtest1(y,lags); + titleString = 'Error LM Test Statistic Values (left) and P-values (right)'; + else + [stat,pval] = ljungbox(y,lags); + titleString = 'Error Ljung-Box Q Statistics (left) and P-values (right)'; + end + + clear_axes(handles) + % 1. Set up the axes and their limits + barUL = max(stat)*1.1; + plotUL = 1.1; + plotLL = 0; + barLL = -max(stat)*.1; + axes(handles.plot_handle); + ax=gca; + axis([0 lags+1 barLL barUL]) + set(ax,'XTickMode', 'auto','YTickMode', 'auto','Units','pixels','Position',[32 37 585 392]); + axes(handles.plot_axes2); + axis([0 lags+1 -.1 1.1]) + ax=gca; + set(ax,'YTickMode','auto','Units','pixels','Position',[32 37 585 392],'YAxisLocation','right'); + + % 2. Draw teh bar graph and establish it's limits + axes(handles.plot_handle); + hold on; + b = bar(stat); + set(b,'EdgeColor',[1 1 1],'FaceColor',[.5 .5 1]) + set(get(b(1),'BaseLine'),'LineWidth',1,'LineStyle','none') + hold on; + h = plot(max(stat)*pval); + set(h,'LineWidth',1,'LineStyle','none','Color',[0 0 0],'Marker','s','MarkerFaceColor',[0 0 0],'MarkerEdgeColor',[0 0 0]); + legend('Statistic Value','P-value','Location','NorthWest') + + % 3. Labels and titles + title(titleString) +end + + +function clear_axes(handles) +axes(handles.plot_handle); +cla +set(handles.plot_handle,'XTick',[],'YTick',[],'Units','pixels','Position',[32 37 585 392]) +title('') +axes(handles.plot_axes2); +cla +set(handles.plot_axes2,'XTick',[],'YTick',[],'Units','pixels','Position',[32 37 585 392]) +title('') diff --git a/GUI/ARMAX_about.fig b/GUI/ARMAX_about.fig new file mode 100644 index 0000000000000000000000000000000000000000..9e2dbc2bd8b9ca76803b713def3767c23a2035ec GIT binary patch literal 7011 zcmb7}S2P=dqsGyyqKcwMZHii<)QF&}W~Ewt?@_y`8KSCoWA70<%px^v)TYEv?Nyt` z4lzO!a{u?blE^eOA;=Hds?ccfh_;~?& zU#XkwycFkE_j9&?=j_Dm;|=5m`*`!}+I#apR^*kE0?H}^rDS;@OG(M|{=Y*;t^=kg zBO_bnAR`Mdn96nYw3=o?+A;~37-@X=&}|AUznRLE~Gb3Y`%E|=Kl$&*Aw=A@Imp8(j(x+aSeK!$3_`4P4`cKiu zqEh$j#l{|F1%iV^8c8h}>-CW3V+hE{x1(KzWVy;NUU!wuawR!N+I9C?ti$GIhP<`S z#pyt<@`!*|Wv;nLyF{meo_7u5xI3|433v8!H`v*>E z))dEDFP5x1D7Z~7o4QoBGdL?;B&;V%tZF$=(i8=_#1l`uIsiYfzMn+MJ=~c8Bi6I~ zT=b6IO-p~ZoOZsfmBU>l{>(=$>U2{CH~F{fAjT@(-VOO5lDTy5Q6m;*0|A3xAx~<~ zWTtD4LLt!A*zWTLJ%*T2%IN$kr$YjC9QcrFH_|HHIAxve=GukiEgiAV!ooP7eR`VPbH84{v=x3h!-a3@nU8hCT5)Zk~X&$hR&5 z&UFuJ@U=kI4P>2~koZVC+!4Mfa8iC%f80cG&2kvl zYz-Oei|SDypr2@N4Rb`KJmf$Pls!3LxW2ncg0yua z%@Hs^47QZAH(u>FrM=7yzRB?6&%)(TPGOg*w+FWLpMY7#Ev#1VDgWVR0 z`k)#qd))X|KY_qp>XJdLq)C`t+Q)qa;p3jg{%ulU%Shk2kdFSK%BfT-wKD@tiqQZ1 zwlDx6$|7V<*kqzf$1=fmf>sc+LR%gjhKC*Wq|Z`(TFD}M1Ar$&n_?VHST0zn*%iHc zc;HYWhqB4a!3>W@wTiy()Jkg9C1O%R*t(DgT?HQ-LOmJNhUE8@bB4XNAKCSK6{uQz z6yrI=_VZd<(5sq8U}CbG4^}4Yv|VZ5h%dT+=Fmsi;;U`V3|mIfvI$#Csb)0!e5;my*H-!~NA1TPQ8V1&86H9v z>1^Q=Qhj}E^WcQ$%3JvqeC<%EPQ@}d&?Kw5*#(WZpD&dbV_-xCKqE$)f)oM7|y>mb2>P~$xIW6NS3Q?L51-tk!?p}YNcjD-wjbFELdnov%^+@7LvJ~M?|=EwoLQvZXV>$PR z=8JB`C6JPcoa;2&A+URJBA;#z0g5wD|q4}JhIc}*GnF5%_7^W z?Gzdq1)yuM;RvIuY9#V0A0)lD=>#Pv;#s)M;E}GmvA(+$Gf`-82S>I5K;+Z#8OMfS zQ@}6QhN7&5jVtWEg(C2 zkRSxtvVu!YAIM-?1hUx(9Bc9g;GZTk_xCEygh z|8e^isAPu7-R?9KDFG?2<^F@}bE(9^km!^9mp2v5O@mdtucpNQDL>2KaKwtAe?YE1 z!Seg+79thlILgfj#7tsOXo0^1t_$~@`dZz3=%lT)7cmGKKM@U~Rb-Ei_#=i#bFy!F zT~I~5M~t(E#={|B(P7J-T>?|IRaBTXo}?SONQL2Zm3{f;daUEf2Ro*B znR(`#KoD6mG$opSoxG$yQ_H{%`p?DVZWN&7ly;eRAMHx5vn-?AX#>d5Xwh#k*g7}c z^xKYY-Uol{un)(|v?WA1$S?OYYE1!tKf*jI_kh`wNJpJ`@3#nf0xsFIeFDQ%$uILNG z9lxkAiaiki8Fm@ADK2J?7@pnWqE(4B4NvTB{M5zHKQ6Z zJOpkXX?!tEnhf#qV1`<#%>RJ4*^ojsHMJb; 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zb5mb1Az&xuGt?0g5wUl8eSdB*+(5d&3-vtY{r%lQr|w@(J(DLG7H+M@c$^N4WmZ^2 z|EM8K9`dXsA}ZTS)hA>?ozd5_0a5P1=Qwveyhel7s{b@lgq7!~KN$FKVnPZDZ0-W_}`nmjuR77G}53rO!UkGzw& zuDvF=mvstiVD6=b-*9dx^fhA^f7DuYlxN=ZX2-1PK%Az+NKGX8N?fj~?P`a7U$byO zl@$L!>6_dMBK2gE99{3@P#Uio;Q~-zyDnf8iK+qLk^Yy_7%{v0jA*loLGcQz 3) + for index = 1:2:(nargin-3), + if nargin-3==index, break, end + switch lower(varargin{index}) + case 'title' + set(hObject, 'Name', varargin{index+1}); + case 'string' + set(handles.text1, 'String', varargin{index+1}); + end + end +end + +% Determine the position of the dialog - centered on the callback figure +% if available, else, centered on the screen +FigPos=get(0,'DefaultFigurePosition'); +OldUnits = get(hObject, 'Units'); +set(hObject, 'Units', 'pixels'); +OldPos = get(hObject,'Position'); +FigWidth = OldPos(3); +FigHeight = OldPos(4); +if isempty(gcbf) + ScreenUnits=get(0,'Units'); + set(0,'Units','pixels'); + ScreenSize=get(0,'ScreenSize'); + set(0,'Units',ScreenUnits); + + FigPos(1)=1/2*(ScreenSize(3)-FigWidth); + FigPos(2)=2/3*(ScreenSize(4)-FigHeight); +else + GCBFOldUnits = get(gcbf,'Units'); + set(gcbf,'Units','pixels'); + GCBFPos = get(gcbf,'Position'); + set(gcbf,'Units',GCBFOldUnits); + FigPos(1:2) = [(GCBFPos(1) + GCBFPos(3) / 2) - FigWidth / 2, ... + (GCBFPos(2) + GCBFPos(4) / 2) - FigHeight / 2]; +end +FigPos(3:4)=[FigWidth FigHeight]; +set(hObject, 'Position', FigPos); +set(hObject, 'Units', OldUnits); + +% Show a question icon from dialogicons.mat - variables questIconData +% and questIconMap +load OxLogo.mat + +IconData=OxLogo; +%questIconMap(256,:) = get(handles.figure1, 'Color'); +%IconCMap=questIconMap; + +Img=image(IconData, 'Parent', handles.axes1); +% set(handles.figure1, 'Colormap', IconCMap); + +set(handles.axes1, ... + 'Visible', 'off', ... + 'YDir' , 'reverse' , ... + 'XLim' , get(Img,'XData'), ... + 'YLim' , get(Img,'YData') ... + ); + +% Make the GUI modal +set(handles.figure1,'WindowStyle','modal') + +% UIWAIT makes ARMAX_about wait for user response (see UIRESUME) +uiwait(handles.figure1); + +% --- Outputs from this function are returned to the command line. +function varargout = ARMAX_about_OutputFcn(hObject, eventdata, handles) +% varargout cell array for returning output args (see VARARGOUT); +% hObject handle to figure +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Get default command line output from handles structure +varargout{1} = handles.output; + +% The figure can be deleted now +delete(handles.figure1); + +% --- Executes on button press in pushbutton1. +function pushbutton1_Callback(hObject, eventdata, handles) +% hObject handle to pushbutton1 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +handles.output = get(hObject,'String'); + +% Update handles structure +guidata(hObject, handles); + +% Use UIRESUME instead of delete because the OutputFcn needs +% to get the updated handles structure. +uiresume(handles.figure1); + +% --- Executes on button press in pushbutton2. +function pushbutton2_Callback(hObject, eventdata, handles) +% hObject handle to pushbutton2 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +handles.output = get(hObject,'String'); + +% Update handles structure +guidata(hObject, handles); + +% Use UIRESUME instead of delete because the OutputFcn needs +% to get the updated handles structure. +uiresume(handles.figure1); + + +% --- Executes when user attempts to close figure1. +function figure1_CloseRequestFcn(hObject, eventdata, handles) +% hObject handle to figure1 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +if isequal(get(handles.figure1, 'waitstatus'), 'waiting') + % The GUI is still in UIWAIT, us UIRESUME + uiresume(handles.figure1); +else + % The GUI is no longer waiting, just close it + delete(handles.figure1); +end + + +% --- Executes on key press over figure1 with no controls selected. +function figure1_KeyPressFcn(hObject, eventdata, handles) +% hObject handle to figure1 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Check for "enter" or "escape" +if isequal(get(hObject,'CurrentKey'),'escape') + % User said no by hitting escape + handles.output = 'No'; + + % Update handles structure + guidata(hObject, handles); + + uiresume(handles.figure1); +end + +if isequal(get(hObject,'CurrentKey'),'return') + uiresume(handles.figure1); +end diff --git a/GUI/ARMAX_close_dialog.fig b/GUI/ARMAX_close_dialog.fig new file mode 100644 index 0000000000000000000000000000000000000000..d03da3b0c3a7557137f0738e6644bc2961680254 GIT binary patch literal 6687 zcmb7|)n5}1pv6H1q(n-Z(cLW!MB+;K)M?VMMAn$8fgJXju7yM#v))H*FMBr+R~cqKB@=ZW zer6>PJ8Lhy56o^58D>LkFJ=XA2WF91%)%lv!qPG#qRgVg!jjDYZ((7pYm;JOVP(={ zVfp3FWjlQ||3@_prbvBaMD|p}usw-1o!Q_mF5!0$*F?iF;$-aJO5}fS_PgT>hjq1p z{o`5W%9)AxBjn8Trf-d?6pbPq^DD%3iPO!F=>^i6r5os56!=gswyY&PMN!4v>p~m`LD#PFK3PF zJ~#(fBZjO3{bfczc##qwgfF!Nu4iv~9Q91*T$kxer6S*TNLscPn&qB-;2e)qhmT%7 zN=V{mpB(S~$|7?m5ZizWli9Zf=3@L5xK?+xk}QuLf=%jp(={SQz)iAUmWy3;xxw%$ zG~v93#jrD`5io|gr`4U`vEx|AKaM+G5>j5#SdF>twA--_oR}7^k`Bv#eEj; 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Starting from the left, property value pairs are +% applied to the GUI before ARMAX_close_dialog_OpeningFunction gets called. An +% unrecognized property name or invalid value makes property application +% stop. All inputs are passed to ARMAX_close_dialog_OpeningFcn via varargin. +% +% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one +% instance to run (singleton)". +% +% See also: GUIDE, GUIDATA, GUIHANDLES + +% Edit the above text to modify the response to help ARMAX_close_dialog + +% Last Modified by GUIDE v2.5 19-Aug-2006 01:03:58 + +% Begin initialization code - DO NOT EDIT +gui_Singleton = 1; +gui_State = struct('gui_Name', mfilename, ... + 'gui_Singleton', gui_Singleton, ... + 'gui_OpeningFcn', @ARMAX_close_dialog_OpeningFcn, ... + 'gui_OutputFcn', @ARMAX_close_dialog_OutputFcn, ... + 'gui_LayoutFcn', [] , ... + 'gui_Callback', []); +if nargin && ischar(varargin{1}) + gui_State.gui_Callback = str2func(varargin{1}); +end + +if nargout + [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); +else + gui_mainfcn(gui_State, varargin{:}); +end +% End initialization code - DO NOT EDIT + +% --- Executes just before ARMAX_close_dialog is made visible. +function ARMAX_close_dialog_OpeningFcn(hObject, eventdata, handles, varargin) +% This function has no output args, see OutputFcn. +% hObject handle to figure +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +% varargin command line arguments to ARMAX_close_dialog (see VARARGIN) + +% Choose default command line output for ARMAX_close_dialog +handles.output = 'Yes'; + +% Update handles structure +guidata(hObject, handles); + +% Insert custom Title and Text if specified by the user +% Hint: when choosing keywords, be sure they are not easily confused +% with existing figure properties. See the output of set(figure) for +% a list of figure properties. +if(nargin > 3) + for index = 1:2:(nargin-3), + if nargin-3==index, break, end + switch lower(varargin{index}) + case 'title' + set(hObject, 'Name', varargin{index+1}); + case 'string' + set(handles.text1, 'String', varargin{index+1}); + end + end +end + +% Determine the position of the dialog - centered on the callback figure +% if available, else, centered on the screen +FigPos=get(0,'DefaultFigurePosition'); +OldUnits = get(hObject, 'Units'); +set(hObject, 'Units', 'pixels'); +OldPos = get(hObject,'Position'); +FigWidth = OldPos(3); +FigHeight = OldPos(4); +if isempty(gcbf) + ScreenUnits=get(0,'Units'); + set(0,'Units','pixels'); + ScreenSize=get(0,'ScreenSize'); + set(0,'Units',ScreenUnits); + + FigPos(1)=1/2*(ScreenSize(3)-FigWidth); + FigPos(2)=2/3*(ScreenSize(4)-FigHeight); +else + GCBFOldUnits = get(gcbf,'Units'); + set(gcbf,'Units','pixels'); + GCBFPos = get(gcbf,'Position'); + set(gcbf,'Units',GCBFOldUnits); + FigPos(1:2) = [(GCBFPos(1) + GCBFPos(3) / 2) - FigWidth / 2, ... + (GCBFPos(2) + GCBFPos(4) / 2) - FigHeight / 2]; +end +FigPos(3:4)=[FigWidth FigHeight]; +set(hObject, 'Position', FigPos); +set(hObject, 'Units', OldUnits); + +% Show a question icon from dialogicons.mat - variables questIconData +% and questIconMap +load dialogicons.mat + +IconData=questIconData; +questIconMap(256,:) = get(handles.figure1, 'Color'); +IconCMap=questIconMap; + +Img=image(IconData, 'Parent', handles.axes1); +set(handles.figure1, 'Colormap', IconCMap); + +set(handles.axes1, ... + 'Visible', 'off', ... + 'YDir' , 'reverse' , ... + 'XLim' , get(Img,'XData'), ... + 'YLim' , get(Img,'YData') ... + ); + +% Make the GUI modal +set(handles.figure1,'WindowStyle','modal') + +% UIWAIT makes ARMAX_close_dialog wait for user response (see UIRESUME) +uiwait(handles.figure1); + +% --- Outputs from this function are returned to the command line. +function varargout = ARMAX_close_dialog_OutputFcn(hObject, eventdata, handles) +% varargout cell array for returning output args (see VARARGOUT); +% hObject handle to figure +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Get default command line output from handles structure +varargout{1} = handles.output; + +% The figure can be deleted now +delete(handles.figure1); + +% --- Executes on button press in pushbutton1. +function pushbutton1_Callback(hObject, eventdata, handles) +% hObject handle to pushbutton1 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +handles.output = get(hObject,'String'); + +% Update handles structure +guidata(hObject, handles); + +% Use UIRESUME instead of delete because the OutputFcn needs +% to get the updated handles structure. +uiresume(handles.figure1); + +% --- Executes on button press in pushbutton2. +function pushbutton2_Callback(hObject, eventdata, handles) +% hObject handle to pushbutton2 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +handles.output = get(hObject,'String'); + +% Update handles structure +guidata(hObject, handles); + +% Use UIRESUME instead of delete because the OutputFcn needs +% to get the updated handles structure. +uiresume(handles.figure1); + + +% --- Executes when user attempts to close figure1. +function figure1_CloseRequestFcn(hObject, eventdata, handles) +% hObject handle to figure1 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +handles.output = 'No'; +guidata(hObject, handles); +if isequal(get(handles.figure1, 'waitstatus'), 'waiting') + % The GUI is still in UIWAIT, us UIRESUME + uiresume(handles.figure1); +else + % The GUI is no longer waiting, just close it + delete(handles.figure1); +end + + +% --- Executes on key press over figure1 with no controls selected. +function figure1_KeyPressFcn(hObject, eventdata, handles) +% hObject handle to figure1 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Check for "enter" or "escape" +if isequal(get(hObject,'CurrentKey'),'escape') + % User said no by hitting escape + handles.output = 'No' + + % Update handles structure + guidata(hObject, handles); + + uiresume(handles.figure1); +end + +if isequal(get(hObject,'CurrentKey'),'return') + uiresume(handles.figure1); +end diff --git a/GUI/ARMAX_viewer.fig b/GUI/ARMAX_viewer.fig new file mode 100644 index 0000000000000000000000000000000000000000..3a4c6e883d90057203f85fbad2ddffc480d583e8 GIT binary patch literal 8388 zcmb7|=Q|q!*T!uvRcdcqYVW=Gs97ya?Ap{QH4=Nz8m0Css#<$fLTcAc?L8_8g4hux z-oDTC{sZs%e7>CPI`{eA_c2g4(N|StmlP6VH&8VZbawM_5@0v-ckN0$wCEEv3+BTE`JSq4d$Ff6$SuV-Pr@AB)v9 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singleton*. +% +% H = ARMAX_viewer returns the handle to a new ARMAX_viewer or the handle to +% the existing singleton*. +% +% ARMAX_viewer('CALLBACK',hObject,eventData,handles,...) calls the local +% function named CALLBACK in ARMAX_viewer.M with the given input arguments. +% +% ARMAX_viewer('Property','Value',...) creates a new ARMAX_viewer or raises the +% existing singleton*. Starting from the left, property value pairs are +% applied to the GUI before ARMAX_viewer_OpeningFunction gets called. An +% unrecognized property name or invalid value makes property application +% stop. All inputs are passed to ARMAX_viewer_OpeningFcn via varargin. +% +% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one +% instance to run (singleton)". +% +% See also: GUIDE, GUIDATA, GUIHANDLES + +% TODO : Add parameter display for hyperparapmeter for distributions +% FIXME: Fix the behavior for very large models + +% Edit the above text to modify the response to help ARMAX_viewer + +% Last Modified by GUIDE v2.5 09-Sep-2006 14:45:09 + +% Begin initialization code - DO NOT EDIT +gui_Singleton = 1; +gui_State = struct('gui_Name', mfilename, ... + 'gui_Singleton', gui_Singleton, ... + 'gui_OpeningFcn', @ARMAX_viewer_OpeningFcn, ... + 'gui_OutputFcn', @ARMAX_viewer_OutputFcn, ... + 'gui_LayoutFcn', [] , ... + 'gui_Callback', []); +if nargin && ischar(varargin{1}) + gui_State.gui_Callback = str2func(varargin{1}); +end + +if nargout + [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:}); +else + gui_mainfcn(gui_State, varargin{:}); +end +% End initialization code - DO NOT EDIT + +% --- Executes just before ARMAX_viewer is made visible. +function ARMAX_viewer_OpeningFcn(hObject, eventdata, handles, varargin) +% This function has no output args, see OutputFcn. +% hObject handle to figure +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +% varargin command line arguments to ARMAX_viewer (see VARARGIN) + +% Choose default command line output for ARMAX_viewer +handles.output = hObject; +handles.Results = varargin{1}; +if length(varargin)==2 + handles.DisplayNumber = varargin{2}; +else + handles.DisplayNumber = length(handles.Results); +end + +% Update handles structure +guidata(hObject, handles); +popup_cell=[]; +for i=1:length(handles.Results); + popup_cell{i}=handles.Results{i}.StringID; +end +set(handles.model_popupmenu,'String',popup_cell) +set(handles.model_popupmenu,'Value',length(handles.Results)) +set(gcf,'Position',[10 10 1000 706]) +% +display_model(handles,hObject); + + + +% UIWAIT makes ARMAX_viewer wait for user response (see UIRESUME) +% uiwait(handles.figure1); + + +% --- Outputs from this function are returned to the command line. +function varargout = ARMAX_viewer_OutputFcn(hObject, eventdata, handles) +% varargout cell array for returning output args (see VARARGOUT); +% hObject handle to figure +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Get default command line output from handles structure +varargout{1} = handles.output; + + +% --- Executes on mouse press over axes background. +function model_axes_ButtonDownFcn(hObject, eventdata, handles) +% hObject handle to model_axes (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + + +function generate_text(handles,hObject); +% Get rid of results not needed +number = handles.DisplayNumber; +results=handles.Results{number}; +% Compute the needed strings +[ParameterString,VariableString]= generate_strings(results); +% Layout the model +[model_layout_info]=model_layout(ParameterString,VariableString,handles); +% Layout the model statistics +[model_stats_layout_info]=model_stats_layout(results,handles); +% Resize the Parameter Estimates Window +[estimate_window]=resize_parameter_estimate_uipanel(handles); +% Layout the column titles and return their position +[title_positions]=title_layout(handles); +% Compute the text elements for the main display and their positions +[text_positions]=compute_text_positions(handles,ParameterString,title_positions); +% Update the results with a flag that the text layout is done and with all +% of the relevant information, also set the handles +handles.Results{number}.ParameterString=ParameterString; +handles.Results{number}.VariableString=VariableString; +handles.Results{number}.model_layout_info=model_layout_info; +handles.Results{number}.model_stats_layout_info=model_stats_layout_info; +handles.Results{number}.estimate_window=estimate_window; +handles.Results{number}.title_position=title_positions; +handles.Results{number}.text_position=text_positions; +handles.Results{number}.TextFinished=true; +guidata(hObject, handles); + + + +function [ParameterString,VariableString]= generate_strings(results); +% Not finished +% TO DO: ARARCH, EGARCH and AGARCH +index=1; + +ParameterString{index}='y_t ='; +c{index}=''; +index=index+1; + +if results.constant + ParameterString{index}='\phi_0'; + VariableString{index}=''; + index=index+1; +end + +if ~isempty(results.ARlags) + if max(results.ARlags)>0 + for i=1:length(results.ARlags) + ParameterString{index}=['\phi_{' num2str(results.ARlags(i)) '}']; + VariableString{index}=['y_{t-' num2str(results.ARlags(i)) '}']; + index=index+1; + end + end +end + + +if ~isempty(results.MAlags) + if max(results.MAlags)>0 + for i=1:length(results.MAlags) + ParameterString{index}=['\theta_{' num2str(results.MAlags(i)) '}']; + VariableString{index}=['\epsilon_{t-' num2str(results.MAlags(i)) '}']; + index=index+1; + end + end +end + +ParameterString{index}=''; +VariableString{index}='\epsilon_t'; + + + + +function [layout_info]=model_layout(ParameterString,VariableString,handles) + +axes(handles.model_axes); +%set(gcf,'Position',[ -3 35 1024 664],'Units','pixels') +%set(ax,'Units','pixels','Position',[134.1200 500.0400 793.6000 120]) +line=0.75; +count=1; + +result = handles.Results{handles.DisplayNumber}; +ModelString = result.StringID; +% Add on the model specific string +final_str{count}=ModelString; +count=count+1; + +%FIX ME, need to worry about no constant! +if result.constant + final_str{count}=[ParameterString{1} ParameterString{2}]; +else + final_str{count}=[ParameterString{1} ParameterString{2} VariableString{2}]; +end + + +xpos=.05; +for i=3:length(ParameterString) + t=text(xpos,line,['$' final_str{count} '+' ParameterString{i} VariableString{i} '$' ],'Interpreter','latex','FontSize',12); + ex=get(t,'Extent'); + delete(t); + if ex(1)+ex(3)<1 + % No problems, add and try next + final_str{count}=[final_str{count} '+' ParameterString{i} VariableString{i}]; + else + %Problem, no not add and start a new line + xpos=.1; + count=count+1; + final_str{count}=['+' ParameterString{i} VariableString{i}]; + end +end + +t=[]; +line=0.75; +for i=1:count; + if i<3 + xpos=.02; + else + xpos=.07; + end + if i>1 + t{i}=text(xpos,line,['$' final_str{i} '$'] ,'Interpreter','latex','FontSize',12); + else + t{i}=text(xpos,line,['$' final_str{i} '$'] ,'FontSize',12); + end + line=line-0.25; +end + +% Now that the text is layed out, the axes and uipanel need to be resized +% accordingly and the text strings need to be vertically repositioned +% axes height is 33* no lines, y position is always 9 +% uipanel height is 33*no lines+24, y position is 650-uiheight +no_lines=length(final_str); +uiHeight = no_lines*33+24; +uiY = 670 - uiHeight; +uiP=get(handles.model_uipanel,'Position'); +uiP(2)=uiY; +uiP(4)=uiHeight; +set(handles.model_uipanel,'Position',uiP); + +axHeight = 33*no_lines; +axY = 9; +axP=get(handles.model_axes,'Position'); +axP(2)=axY; +axP(4)=axHeight; +set(handles.model_axes,'Position',axP); + +% Finally uniformly distribute the t{i} between at +% [1:no_lines]/(no_lines+1) +positions = (no_lines:-1:1)/(no_lines+1); +for i=1:no_lines; + tP=get(t{i},'Position'); + tP(2)=positions(i); + set(t{i},'Position',tP); +end + +% Need to return everything needed to make relayout easy: +% uipanle position +% axes position +% text strings +% text string position +layout_info.model_uipanel_position = get(handles.model_uipanel,'Position'); +layout_info.model_axes_position = get(handles.model_axes,'Position'); +layout_info.model_text_strings = final_str; +for i=1:length(final_str); + layout_info.model_text_strings_position{i}=get(t{i},'Position'); +end +% Clear the axis +cla + + + + + + +function [layout_info]=model_stats_layout(results,handles) +% 1. Fix the position of and size of the UI and axes +% 2. Layout the important stats and their labels + +axes(handles.stats_axes); +set(handles.stats_axes,'Position',[15 9 920 60]) +model_uipanel_position=get(handles.model_uipanel ,'Position'); +set(handles.model_stats_uipanel,'Position',[25 model_uipanel_position(2)-84 950 84]) + +titles={'Log-likelihood','No. of Params',' Akaike IC','Schwartz/Bayesian IC','$\hat{\sigma}^2$'}; +positions=linspace(.02,.9,length(titles)); +total_space=0; +for i=1:length(titles) + if i==5 + t(i)=text(positions(i),.66,titles{i},'FontName','Tahoma','FontSize',10,'Interpreter','latex'); + else + t(i)=text(positions(i),.66,titles{i},'FontName','Tahoma','FontSize',10); + end + ex(i,:)=get(t(i),'Extent'); + if i>1 + total_space=total_space+ex(i,1)-(ex(i-1,3)+ex(i-1,1)); + end +end +total_space=total_space+.98-(ex(5,3)+ex(5,1)); +% Compute the total amount of space between the objects and uniformly +% respace them +spaces=[4 4 4 4]*total_space/22; +for i=2:length(titles) + ex=get(t(i-1),'Extent'); + set(t(i),'Position',[ex(1)+ex(3)+spaces(i-1) .66 0]); +end + +% Set up the text strings. I need to limit the width +data{1}=sprintf('%0.7g',results.ll); +data{2}=num2str(results.K); +data{3}=sprintf('%0.7g',results.AIC); +data{4}=sprintf('%0.7g',results.BIC); +data{5}=sprintf('%0.7g',results.seregression); + + +for i=1:5 + d(i)=text(positions(i),.33,data{i},'FontName','Tahoma','FontSize',10); + % Now move it so that it is right aligned + p1 = get(d(i),'Extent'); + p2 = get(t(i),'Extent'); + set(d(i),'Position',[p2(1)+p2(3)-p1(3) .33 0]); +end +AX=axis; +hold on; +for i=1:5 + % Now move it so that it is right aligned + p2 = get(t(i),'Extent'); + axis(AX); + x_line_data{i}=[p2(1) p2(1)+p2(3)]'; + y_line_data{i}=[p2(2) p2(2)]; + plot([p2(1) p2(1)+p2(3)],[p2(2) p2(2)],'k'); +end +hold off; + +% Need to return all of teh strings along with all of their positions +layout_info.Titles=titles; +layout_info.Data=data; +layout_info.TitlePosition=[]; +layout_info.DataPosition=[]; + +for i=1:5; + layout_info.TitleHandles{i}=t(i); + layout_info.TitlePosition{i}=get(t(i),'Position'); + layout_info.DataHandle{i}=d(i); + layout_info.DataPosition{i}=get(d(i),'Position'); +end +layout_info.model_stats_uipanel_position = get(handles.model_stats_uipanel,'Position'); +layout_info.stats_axes_position = get(handles.stats_axes,'Position'); +layout_info.x_line_data=x_line_data; +layout_info.y_line_data=y_line_data; +% Clear the axis +cla + + +% --- Executes on selection change in model_popupmenu. +function model_popupmenu_Callback(hObject, eventdata, handles) +% hObject handle to model_popupmenu (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hints: contents = get(hObject,'String') returns model_popupmenu contents as cell array +% contents{get(hObject,'Value')} returns selected item from model_popupmenu +handles.DisplayNumber = get(hObject,'Value'); +guidata(hObject, handles); +display_model(handles,hObject); + +% --- Executes during object creation, after setting all properties. +function model_popupmenu_CreateFcn(hObject, eventdata, handles) +% hObject handle to model_popupmenu (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles empty - handles not created until after all CreateFcns called + +% Hint: popupmenu controls usually have a white background on Windows. +% See ISPC and COMPUTER. +if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) + set(hObject,'BackgroundColor','white'); +end + + + +function page_number_edit_Callback(hObject, eventdata, handles) +% hObject handle to page_number_edit (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hints: get(hObject,'String') returns contents of page_number_edit as text +% str2double(get(hObject,'String')) returns contents of page_number_edit as a double +val = get(hObject,'String'); +result = handles.Results{handles.DisplayNumber}; +LastPage = handles.LastPage; +NumberOfPages = size(result.text_position.x_pos,3); +[CurrentPage, OK] = bounded_integer_validate(val,LastPage,1,NumberOfPages); +if ~OK + set(hObject,'String',num2str(CurrentPage)); +end +draw_parameter_table(result,CurrentPage,handles) +handles.LastPage=CurrentPage; +% Update handles structure +guidata(hObject, handles); + + +% --- Executes during object creation, after setting all properties. +function page_number_edit_CreateFcn(hObject, eventdata, handles) +% hObject handle to page_number_edit (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles empty - handles not created until after all CreateFcns called + +% Hint: edit controls usually have a white background on Windows. +% See ISPC and COMPUTER. +if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) + set(hObject,'BackgroundColor','white'); +end + + + +function num_pages_text_Callback(hObject, eventdata, handles) +% hObject handle to num_pages_text (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) + +% Hints: get(hObject,'String') returns contents of num_pages_text as text +% str2double(get(hObject,'String')) returns contents of num_pages_text as a double + + +% --- Executes during object creation, after setting all properties. +function num_pages_text_CreateFcn(hObject, eventdata, handles) +% hObject handle to num_pages_text (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles empty - handles not created until after all CreateFcns called + +% Hint: edit controls usually have a white background on Windows. +% See ISPC and COMPUTER. +if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) + set(hObject,'BackgroundColor','white'); +end + + +% --- Executes on button press in increase_page_pushbutton. +function increase_page_pushbutton_Callback(hObject, eventdata, handles) +% hObject handle to increase_page_pushbutton (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +result = handles.Results{handles.DisplayNumber}; +NumberOfPages = size(result.text_position.x_pos,3); +CurrentPage = str2double(get(handles.page_number_edit,'String')); +if CurrentPage < NumberOfPages + CurrentPage = CurrentPage +1; + set(handles.page_number_edit,'String',num2str(CurrentPage)); + + draw_parameter_table(result,CurrentPage,handles) + handles.LastPage=CurrentPage; + % Update handles structure + guidata(hObject, handles); + +end + +% --- Executes on button press in decrease_page_pushbutton. +function decrease_page_pushbutton_Callback(hObject, eventdata, handles) +% hObject handle to decrease_page_pushbutton (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +result = handles.Results{handles.DisplayNumber}; +CurrentPage = str2double(get(handles.page_number_edit,'String')); +if CurrentPage >1 + CurrentPage = CurrentPage - 1; + set(handles.page_number_edit,'String',num2str(CurrentPage)); + + draw_parameter_table(result,CurrentPage,handles) + handles.LastPage=CurrentPage; + % Update handles structure + guidata(hObject, handles); +end + +% --- Executes on button press in pushbutton3. +function pushbutton3_Callback(hObject, eventdata, handles) +% hObject handle to pushbutton3 (see GCBO) +% eventdata reserved - to be defined in a future version of MATLAB +% handles structure with handles and user data (see GUIDATA) +delete(handles.figure1) + + + + +function [window_stats]=resize_parameter_estimate_uipanel(handles) +model_uipanel_pos=get(handles.model_stats_uipanel,'Position'); +estimates_uipanel_pos=get(handles.estimates_uipanel ,'Position'); +estimates_uipanel_pos(4)=estimates_uipanel_pos(4)+model_uipanel_pos(2)-sum(estimates_uipanel_pos([2 4])); +set(handles.estimates_uipanel ,'Position',estimates_uipanel_pos); + +estimates_axes_pos=get(handles.estimates_axes,'Position'); +estimates_axes_pos(2)=12; +set(handles.estimates_axes,'Position',estimates_axes_pos) + +estimates_uipanel_pos=get(handles.estimates_uipanel ,'Position'); +estimates_axes_pos=get(handles.estimates_axes,'Position'); +estimates_axes_pos(4)=estimates_uipanel_pos(4)-24; +set(handles.estimates_axes,'Position',estimates_axes_pos); +estimates_axes_pos=get(handles.estimates_axes,'Position'); +% Note, I want ot make sure that the estimates window is at least 330 +% pixels high + +% FIXME: Fix the behavior for very large models +% ScreenSize = get(0,'ScreenSize') +% set(handles.figure1,'Position',[1 ScreenSize-HeightofWindow-33 WidthofWindow HeightofWindow]) +% Return the position of the uipanel, the axes and the figure! +window_stats.axes_pos=estimates_axes_pos; +window_stats.uipanel_pos=estimates_uipanel_pos; +window_stats.figure_pos=get(handles.figure1,'Position'); + + + + + +function [title_position]=title_layout(handles) +titles={'Parameter','Estimate','Std. Error','T-stat','P-val'}; +axes(handles.estimates_axes); +t(1)=text(.02,.5,titles{1},'FontName','Tahoma','FontSize',10); +axes_pos=get(handles.estimates_axes,'Position'); +set(t(1),'Units','pixels'); +t_pos=get(t(1),'Position'); +t_ex = get(t(1),'Extent'); +y=floor(axes_pos(4)-t_ex(4)/2-10); +t_pos(2)=y; +set(t(1),'Position',t_pos) +position{1}=t_pos; +for i=2:length(titles); + t(i)=text((i-1)/6+.02,.5,titles{i},'FontName','Tahoma','FontSize',10); + set(t(i),'Units','pixels') ; + t_pos=get(t(i),'Position'); + t_pos(2)=y; + set(t(i),'Position',t_pos); + position{i}=t_pos; +end +AX=axis; +hold on; +for i=1:length(titles) + % Now move it so that it is right aligned + set(t(i),'Units','normalized'); + p2 = get(t(i),'Extent'); + % Need to get the right points of each label to do right alignment + right_points{i}=p2(1)+p2(3); + axis(AX); + x_plot{i}=[p2(1) p2(1)+p2(3)]; + y_plot{i}=[p2(2) p2(2)]'; + plot(x_plot{i},y_plot{i},'k'); +end + +hold off; +tt=text(.5,.5,'$\alpha \beta \gamma \lambda \omega \nu \mu$','Interpreter','latex','FontSize',14); +row_height=get(tt,'Extent'); +delete(tt); +row_height=row_height(4); +title_position.Titles=titles; +title_position.TitlePosition=position; +title_position.x_line_data=x_plot; +title_position.y_line_data=y_plot; +title_position.RowHeight=row_height; +title_position.NumRows=floor((1-0.5*row_height)/row_height); +title_position.RightPoints=right_points; +% Clear the axis +cla + + +function [text_positions]=compute_text_positions(handles,str,title_position) +% First set up the texts + +results = handles.Results{handles.DisplayNumber}; +right_points = title_position.RightPoints; +actual_rows=title_position.NumRows-1; +for i=2:length(str)-1 + % first compute the page + page = ceil((i-1)/actual_rows); + + if mod(i-1,actual_rows)==0 + table_position = actual_rows; + else + table_position = mod(i-1,actual_rows); + end + for j=1:5 + switch j + case 1 + % Latex string + window_text{table_position,j,page} = ['$' str{i} '$']; + case 2 + % Estimate + temp = results.parameters(i-1); + case 3 + % Estimate + temp = results.StdErr(i-1); + case 4 + % Estimate + temp = results.Tstat(i-1); + case 5 + % Estimate + temp = results.Pval(i-1); + end + if j~=1 + if temp<.000001 + window_text{table_position,j,page} = sprintf('%0.3g',temp); + else + window_text{table_position,j,page} = sprintf('%0.5f',temp); + end + end + end + if mod(i-1,actual_rows)==0 + actual_position = actual_rows+1; + else + actual_position = mod(i-1,actual_rows)+1; + end + row_height=title_position.RowHeight; + for j=1:5 + y_pos{table_position,j,page} = 1-(actual_position)*row_height; + if j==1 + temp_text =text(.5,y_pos{table_position,j,page},window_text{table_position,j,page},'Interpreter','latex','FontSize',12); + else + temp_text =text(.5,y_pos{table_position,j,page},window_text{table_position,j,page},'FontName','Tahoma','FontSize',10); + end + ex=get(temp_text,'Extent'); + delete(temp_text); + x_pos{table_position,j,page}=right_points{j}-ex(3); + end +end +% Set up the return data +text_positions.x_pos = x_pos; +text_positions.y_pos = y_pos; +text_positions.window_text = window_text; + +function draw_data(result,handles,hObject) +% Resize the figure +set(handles.figure1,'Position',result.estimate_window.figure_pos); +% Resize the uipanels +set(handles.model_uipanel,'Position',result.model_layout_info.model_uipanel_position); +set(handles.model_stats_uipanel,'Position',result.model_stats_layout_info.model_stats_uipanel_position); +set(handles.estimates_uipanel,'Position',result.estimate_window.uipanel_pos) +% Resize the axes +set(handles.model_axes,'Position',result.model_layout_info.model_axes_position); +set(handles.stats_axes ,'Position',result.model_stats_layout_info.stats_axes_position); +set(handles.estimates_axes,'Position',result.estimate_window.axes_pos); +% Draw the model +axes(handles.model_axes) +% Make sure itis clear +cla +str = result.model_layout_info.model_text_strings; +pos = result.model_layout_info.model_text_strings_position; +N = length(str); +for i=1:N + x=pos{i}(1); + y=pos{i}(2); + if i>1 + text(x,y,['$' str{i} '$'],'Unit','normalized','interpreter','latex','FontSize',12) + else + text(x,y,[str{i}],'Unit','normalized','FontSize',12) + end +end +% Draw the model statistic titles, lines, and values +axes(handles.stats_axes) +% Make sure itis clear +cla +str = result.model_stats_layout_info.Titles; +pos = result.model_stats_layout_info.TitlePosition; +N = length(str); +for i=1:N + x=pos{i}(1); + y=pos{i}(2); + if i~=5 + text(x,y,str{i},'Unit','normalized','FontSize',10,'FontName','Tahoma') + else + text(x,y,str{i},'Unit','normalized','FontSize',10,'FontName','Tahoma','Interpreter','latex') + end +end +hold on; +for i=1:N + % Now move it so that it is right aligned + x=result.model_stats_layout_info.x_line_data{i}; + y=result.model_stats_layout_info.y_line_data{i}; + plot(x,y,'k'); +end +hold off; +str = result.model_stats_layout_info.Data; +pos = result.model_stats_layout_info.DataPosition; +N = length(str); +for i=1:N + x=pos{i}(1); + y=pos{i}(2); + text(x,y,str{i},'Unit','normalized','FontSize',10,'FontName','Tahoma') +end +% Call the function to draw the correct page, presumably one +draw_parameter_table(result,1,handles) % In the initial draw we will always draw page 1 + +handles.LastPage=1; +% Update handles structure +guidata(hObject, handles); + + +% Finally update the UI elements that have to do with the pages +NumberOfPages = size(result.text_position.x_pos,3); +if NumberOfPages==1 + % Easy case + set(handles.page_number_edit,'BackgroundColor',[0.5 0.5 0.5],'String','1') + set(handles.increase_page_pushbutton,'Enable','off') + set(handles.decrease_page_pushbutton,'Enable','off') + set(handles.number_of_pages_text,'String',num2str(NumberOfPages)); +else + set(handles.page_number_edit,'BackgroundColor',[1 1 1],'String','1') + set(handles.increase_page_pushbutton,'Enable','on') + set(handles.decrease_page_pushbutton,'Enable','on') + set(handles.number_of_pages_text,'String',num2str(NumberOfPages)); +end + + + + + + +function draw_parameter_table(result,page,handles) +axes(handles.estimates_axes) +% Make sure it is clear +cla +% Draw the column titles +str = result.title_position.Titles; +pos = result.title_position.TitlePosition; +N = length(str); +for i=1:N + x=pos{i}(1); + y=pos{i}(2); + text(x,y,str{i},'Unit','pixel','FontSize',10,'FontName','Tahoma') +end +% Draw the lines +hold on; +for i=1:N + % Now move it so that it is right aligned + x=result.title_position.x_line_data{i}; + y=result.title_position.y_line_data{i}; + plot(x,y,'k'); +end +hold off; +x = result.text_position.x_pos(:,:,page); +y = result.text_position.y_pos(:,:,page); +str = result.text_position.window_text(:,:,page); + +N = size(x,1); + +for i=1:N + for j=1:5 + % Draw the data on the correct page + if j==1 + text(x{i,j},y{i,j},str{i,j},'Interpreter','latex','FontSize',12); + else + text(x{i,j},y{i,j},str{i,j},'FontName','Tahoma','FontSize',10); + end + end +end + + + +function display_model(handles,hObject) +% Check to see if the moodel has been processed. If it has, go striaght to +% the draw model, else compute te strings then draw the model +results = handles.Results{handles.DisplayNumber}; +if isfield(results,'TextFinished') + draw_data(results,handles,hObject) +else + % Generate the text labels + generate_text(handles,hObject); + % update handles + handles = guidata(hObject); + results = handles.Results{handles.DisplayNumber}; + % Draw the labels + draw_data(results,handles,hObject) +end + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Function to do integer vallidation for ACF Lags +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +function [val, OK] = bounded_integer_validate(val,orig_val,LB,UB) +val = str2double(val); +% Test cases +% Nan: return old value and OK=0 +% <0 return 0 and OK=0 +% + but not 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z3v3EpM;sBMeG*_{KW&4)VJPP%H2!yyr~gl$+54tOMowTRoTNvAbELfphy7sWs4fuo Y0bxr1-rbHS;A+|MvXEdVx{!DO2j(RDzyJUM literal 0 HcmV?d00001 diff --git a/addToPath.m b/addToPath.m new file mode 100644 index 0000000..ac716f3 --- /dev/null +++ b/addToPath.m @@ -0,0 +1,73 @@ +function addToPath(arg) + +% Adds the MFE Toolbox to the current path and optionally saves the path +silent = false; +if nargin>0 && strcmpi(arg,'-silent') + silent = true; +end + +dirList = {'bootstrap',... + 'crosssection',... + 'distributions',... + 'GUI',... + 'multivariate',... + 'tests',... + 'timeseries',... + 'univariate',... + 'utility',... + 'realized',... + }; +optionalDirList = {'duplication'}; +mexDir = 'dlls'; + +for i=1:length(dirList) + addpath(fullfile(pwd,dirList{i})); +end + + +user_entry = ''; +while ~ismember({user_entry},{'Y','N'}) && ~silent + user_entry = input('Add MATLAB work-a-like functions? [Y/N(default)] ','s'); + user_entry = upper(user_entry); + if isempty(user_entry) + user_entry = 'N'; + end +end + +if strcmpi(user_entry,'Y') + for i=1:length(optionalDirList) + addpath(fullfile(pwd,optionalDirList{i})); + end +end + +user_entry = ''; +while ~ismember({user_entry},{'Y','N'}) && ~silent + user_entry = input('Make path permanent? [Y/N (default)] ','s'); + user_entry = upper(user_entry); + if isempty(user_entry) + user_entry = 'N'; + end +end + +if strcmpi(user_entry,'Y') + try + savepath + catch ME + warning('MFEToolbox:Path',['There was a problem saving the path. The error was: \n' ME.message]) + end +end + +if strcmpi(computer,'PCWIN64') + user_entry = ''; + while ~ismember({user_entry},{'Y','N'}) && ~silent + user_entry = input('Add MEX files to path? [Y(default)/N] ','s'); + user_entry = upper(user_entry); + if isempty(user_entry) + user_entry = 'Y'; + end + end + if strcmp(user_entry,'Y') || silent + addpath(fullfile(pwd,mexDir)); + end +end + diff --git a/bootstrap/block_bootstrap.m b/bootstrap/block_bootstrap.m new file mode 100644 index 0000000..95ecc7b --- /dev/null +++ b/bootstrap/block_bootstrap.m @@ -0,0 +1,77 @@ +function [bsdata, indices]=block_bootstrap(data,B,w) +% Implements a circular block bootstrap for bootstrapping stationary, dependant series +% +% USAGE: +% [BSDATA, INDICES]=block_bootstrap(DATA,B,W) +% +% INPUTS: +% DATA - T by 1 vector of data to be bootstrapped +% B - Number of bootstraps +% W - Block length +% +% OUTPUTS: +% BSDATA - T by B matrix of bootstrapped data +% INDICES - T by B matrix of locations of the original BSDATA=DATA(indexes); +% +% COMMENTS: +% To generate bootstrap sequences for other uses, such as bootstrapping vector processes, +% simpleset DATA to (1:N)' +% +% See also stationary_bootstrap + +% Author: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 2 Date: 12/31/2001 + + +%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=3 + error('3 inputs required') +end +% Get the length of the data +[t,k]=size(data); +if k>1 + error('DATA must be a column vector') +end +if t<2 + error('DATA must have at least 2 observations.') +end +if ~isscalar(w) || w<1 || floor(w)~=w + error('W must be a positive scalar integer') +end +if ~isscalar(B) || B<1 || floor(B)~=B + error('B must be a positive scalar integer') +end +%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%% + +% Make it easy to do the circular bootstrap +data=[data;data(1:w-1)]; +% Compute the number of blocks needed +s=ceil(t/w); +% Generate the starting points +Bs=floor(rand(s,B)*t)+1; +indices=zeros(s*w,B); +index=1; +% Adder is a variable that needs to be added each loop +adder=repmat((0:w-1)',1,B); +for i=1:w:t + indices(i:(i+w-1),:)=repmat(Bs(index,:),w,1)+adder; + index=index+1; +end +indices=indices(1:t,:); +bsdata=data(indices); + + + + + + + + + + + diff --git a/bootstrap/bsds.m b/bootstrap/bsds.m new file mode 100644 index 0000000..be9ce32 --- /dev/null +++ b/bootstrap/bsds.m @@ -0,0 +1,176 @@ +function [c,u,l]=bsds(bench,models,B,w,type,boot) +% Calculate Whites and Hansens p-vals for out-performance using unmodified data or studentized +% residuals, the latter often providing better power, particularly when the losses functions are +% heteroskedastic +% +% USAGE: +% [C] = bsds_studentized(BENCH,MODELS,B,W) +% [C,U,L] = bsds_studentized(BENCH,MODELS,B,W,TYPE,BOOT) +% +% INPUTS: +% BENCH - Losses from the benchmark model +% MODELS - Losses from each of the models used for comparrison +% B - Number of Bootstrap replications +% W - Desired block length +% TYPE - String, either 'STANDARD' or 'STUDENTIZED'. 'STUDENTIZED' is the default, and +% generally leads to better power. +% BOOT - [OPTIONAL] 'STATIONARY' or 'BLOCK'. Stationary is used as the default. +% +% OUTPUTS: +% C - Consistent P-val(Hansen) +% U - Upper P-val(White) (Original RC P-vals) +% L - Lower P-val(Hansen) +% +% COMMENTS: +% This version of the BSDS operates on quantities that should be 'bads', such as losses. The null +% hypothesis is that the average performance of the benchmark is as small as the minimum average +% performance across the models. The alternative is that the minimum average loss across the +% models is smaller than the the average performance of the benchmark. +% +% If the quantities of interest are 'goods', such as returns, simple call bsds_studentized with +% -1*BENCH and -1*MODELS +% +% EXAMPLES: +% Standard Reality Check with 1000 bootstrap replications and a window size of 12 +% bench = randn(1000,1).^2; +% models = randn(1000,100).^2; +% [c,realityCheckPval] = bsds(bench, models, 1000, 12) +% Standard Reality Check with 1000 bootstrap replications, a window size of 12 and a circular +% block bootstrap +% [c,realityCheckPval] = bsds(bench, models, 1000, 12, 'BLOCK') +% Hansen's P-values +% SPAPval = bsds(bench, models, 1000, 12) +% Both Pvals on "goods" +% bench = .01 + randn(1000,1); +% models = randn(1000,100); +% [SPAPval,realityCheckPval] = bsds(-bench, -models, 1000, 12) +% +% See also MCS + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 4/1/2007 + +%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin<4 || nargin>6 + error('4 to inputs required') +end +if nargin == 4 + boot = 'STATIONARY'; + type = 'STUDENTIZED'; +elseif nargin == 5 + boot = 'STATIONARY'; +end +if isempty(type) + type = 'STUDENTIZED'; +end +if strcmpi(type,'STUDENTIZED') + isStudentized = true; +else + isStudentized = false; +end +% Get the length of the data +[tb,kb]=size(bench); +if kb>1 + error('BENCH must be a column vector') +end +if tb<2 + error('BENCH must have at least 2 observations.') +end +[t,k]=size(models); +if t~=tb + error('BENCH and MODELS must have the same number of observations.') +end +if ~isscalar(B) || B<1 || floor(B)~=B + error('B must be a positive scalar integer') +end +if ~isscalar(w) || w<1 || floor(w)~=w + error('W must be a positive scalar integer') +end +boot = upper(boot); +if ~ismember(boot,{'STATIONARY','BLOCK'}) + error('BOOT must be either ''STATIONARY'' or ''BLOCK''.') +end +%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%% +if strcmp(boot,'BLOCK') + bsdata=block_bootstrap((1:t)',B,w); +else + bsdata=stationary_bootstrap((1:t)',B,w); +end + +%OK now we have the bootstraps, what to do with them? +diffs=models-repmat(bench,1,k); + +% First compute the boostarap sample averages, db* +% Second compute the variance estimate, omegak +% First the weghts +q=1/w; +i=1:t-1; +kappa=((t-i)./t).*(1-q).^i+i./t.*(1-q).^(t-i); +% Next compute the variances +vars=zeros(k,1)'; +for i=1:k + workdata = diffs(:,i)-mean(diffs(:,i)); + vars(i)= workdata'*workdata/t; + for j=1:t-1 + vars(i) = vars(i) + 2*kappa(j)*(workdata(1:t-j)'*workdata(j+1:t))/t; + end +end + +% Aold is the original method to compute the truncation point +Aold=1/4*t^(0.25)*sqrt(vars/t); +mean(Aold); +% A new used the log(log(t)) rule +Anew = sqrt((vars/t)*2*log(log(t))); + +% Only recenter if the average is reasonably small or the model is better +% (in which case mean(diffs) is negative). If it is unreasonably large set +% the mean adjustment to 0 +gc=mean(diffs).*(mean(diffs)5 + error('4 or 5 inputs required') +end +if nargin == 4 + boot = 'STATIONARY'; +end +% Get the length of the data +t=size(losses,1); +if t<2 + error('LOSSES must have at least 2 observations.') +end +if ~isscalar(alpha) || alpha>=1 || alpha<=0 + error('ALPHA must be a scalar between 0 and 1') +end +if ~isscalar(B) || B<1 || floor(B)~=B + error('B must be a positive scalar integer') +end +if ~isscalar(w) || w<1 || floor(w)~=w + error('W must be a positive scalar integer') +end +boot = upper(boot); +if ~ismember(boot,{'STATIONARY','BLOCK'}) + error('BOOT must be either ''STATIONARY'' or ''BLOCK''.') +end +%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%% + +% 1. Compute the indices to use throughout the proceedure +if strcmp(boot,'BLOCK') + [bsdata]=block_bootstrap((1:t)',B,w); +else + [bsdata]=stationary_bootstrap((1:t)',B,w); +end + +% All of these values cab be computed once +M0=size(losses,2); +% The i,j element contains the l(i,t)-l(j,t) +dijbar=zeros(M0,M0); +for j=1:M0 + dijbar(j,:) = mean(losses - repmat(losses(:,j),1,M0)); +end +% for each j, compute dij*-bar using the BSdata, than the compute +% var(dijbar) +% 2(a) +dijbarstar=zeros(M0,M0,B); +for b=1:B + meanworkdata=mean(losses(bsdata(:,b),:)); + for j=1:M0 + % The i,j element contains the l(b,i,t)-l(b,j,t) + dijbarstar(j,:,b) = meanworkdata - meanworkdata(j); + end +end +% 2(a) +vardijbar = mean((dijbarstar-repmat(dijbar,[1 1 B])).^2,3); +vardijbar = vardijbar+diag(ones(M0,1)); +% 2(b) depends on the det of models under conderations, so it will have to +% go in the loop + +% These values are used in the empirical distributions an do not depend on +% teh number of models +z0=(dijbarstar-repmat(dijbar,[1 1 B]))./repmat(sqrt(vardijbar),[1 1 B]); +zdata0=dijbar./sqrt(vardijbar); +% Only these depend on teh set of selected models +excludedR=zeros(M0,1); +pvalsR=ones(M0,1); +for i=1:M0-1 + included=setdiff(1:M0,excludedR); + m=length(included); + z=z0(included,included,:); + % Max over the abs value of z in each matrix + empdistTR=squeeze(max(max(abs(z),[],1),[],2)); + zdata=zdata0(included,included); + TR=max(max(zdata)); + pvalsR(i)=mean(empdistTR>TR); + % Finally compute the model to remove, which depends on the maximum + % standardized average (among the remaining models) + % 1. compute dibar + dibar=mean(dijbar(included,included),1)*(m/(m-1)); + % 2. compute var(dibar) + dibstar=squeeze(mean(dijbarstar(included,included,:),1))*(m/(m-1)); + vardi=mean((dibstar'-repmat(dibar,B,1)).^2); + t=dibar./sqrt(vardi); + % Remove the max of t + [temp,modeltoremove] = max(t); + excludedR(i)=included(modeltoremove); +end +% The MCS pval is the max up to that point +maxpval=pvalsR(1); +for i=2:M0 + if pvalsR(i) alpha +pl=find(pvalsR>=alpha,1,'first'); +includedR=excludedR(pl:M0); +excludedR=excludedR(1:pl-1); + + +excludedSQ=zeros(M0,1); +pvalsSQ=ones(M0,1); +for i=1:M0-1 + included=setdiff(1:M0,excludedSQ); + m=length(included); + z=z0(included,included,:); + % Only supposed to sub every element once. Instead sum twice and + % divide by 2 in each matrix (B of them) + empdistTSQ=squeeze(sum(sum(z.^2))/2); + + zdata=zdata0(included,included); + TSQ=sum(sum(zdata.^2))/2; + + pvalsSQ(i)=mean(empdistTSQ>TSQ); + % Finally compute the model to remove, which depends on the maximum + % standardized average (among the remaining models) + % 1. compute dibar + dibar=mean(dijbar(included,included),1)*(m/(m-1)); + % 2. compute var(dibar) + dibstar=squeeze(mean(dijbarstar(included,included,:),1))*(m/(m-1)); + vardi=mean((dibstar'-repmat(dibar,B,1)).^2); + t=dibar./sqrt(vardi); + % Remove the max of t + [temp,modeltoremove] = max(t); + excludedSQ(i)=included(modeltoremove); +end +% The MCS pval is the max up to that point +maxpval=pvalsSQ(1); +for i=2:M0 + if pvalsSQ(i) alpha +pl=find(pvalsSQ>=alpha,1,'first'); +includedSQ=excludedSQ(pl:M0); +excludedSQ=excludedSQ(1:pl-1); diff --git a/bootstrap/robustvcv.m b/bootstrap/robustvcv.m new file mode 100644 index 0000000..fa499b4 --- /dev/null +++ b/bootstrap/robustvcv.m @@ -0,0 +1,82 @@ +function [VCV,A,B,scores,hess,gross_scores]=robustvcv(fun,theta,nw,varargin) +% Compute Robust Variance Covariance matrix numerically, including +% Newey-West style score covariance using 2-sided derivatives +% +% USAGE: +% [VCV,A,B,SCORES,HESS,GROSS_SCORES]=robustvcv(FUN,THETA,NW,VARARGIN) +% +% INPUTS: +% FUN - Function name ('fun') or function handle (@fun) which will +% return the sum of the log-likelihood (scalar) as the 1st output and the individual +% log likelihoods (T by 1 vector) as the second output. +% THETA - Parameter estimates at the optimum, usually from fmin* +% NW - Number of lags to consider in Newey-West covariance. +% Normally set to 0 +% VARARGIN - Other inputs to the log-likelihood function, such as data +% +% OUTPUTS: +% VCV - Estimated robust covariance matrix (see White 1994) +% A - A portion of robust covariance +% B - B portion of robust covariance +% SCORES - T x num_parameters matrix of scores +% HESS - Estimated Hessian (Expectation of second derivative) +% GROSS_SCORES - Numerical scores (1 by num_parameters) of the objective function, usually for diagnostics +% +% COMMENTS: +% This function simplifies calculating sandwich covariance estimators for (Q)MLE estimation + + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 9/1/2005 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if size(theta,1)1 + error('DATA must be a column vector') +end +if t<2 + error('DATA must have at least 2 observations.') +end +if ~isscalar(w) || w<=0 + error('W must be a positive scalar.') +end +if ~isscalar(B) || B<1 || floor(B)~=B + error('B must be a positive scalar integer') +end +%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%% + +% Define the probability of a new block +p=1/w; +% Set up the bsdata and indices +indices=zeros(t,B); +% Initial positions +indices(1,:)=ceil(t*rand(1,B)); +% Set up the random numbers +select=rand(t,B)p) or move to a new starting value + % (rand t +data=[data;data]; +% The indices make finding the bsdata simple +bsdata=data(indices); \ No newline at end of file diff --git a/crosssection/ols.m b/crosssection/ols.m new file mode 100644 index 0000000..8014464 --- /dev/null +++ b/crosssection/ols.m @@ -0,0 +1,128 @@ +function [b, tstat, s2, vcv, vcvwhite, R2, Rbar, yhat] = ols(y,x,c) +% Linear regression estimation with homoskedasticity and White heteroskedasticity robust standard +% errors. +% +% USAGE: +% [B,TSTAT,S2,VCV,VCV_WHITE,R2,RBAR,YHAT] = ols(Y,X,C) +% +% INPUTS: +% Y - N by 1 vector of dependent data +% X - N by K vector of independent data +% C - 1 or 0 to indicate whether a constant should be included (1: include constant) +% +% OUTPUTS: +% B - A K(+1 is C=1) vector of parameters. If a constant is included, it is the first +% parameter. +% TSTAT - A K(+1) vector of t-statistics computed using White heteroskedasticity robust +% standard errors. +% S2 - Estimated error variance of the regression. +% VCV - Variance covariance matrix of the estimated parameters. (Homoskedasticity assumed) +% VCVWHITE - Heteroskedasticity robust VCV of the estimated parameters. +% R2 - R-squared of the regression. Centered if C=1. +% RBAR - Adjusted R-squared. Centered if C=1. +% YHAT - Fit values of the dependent variable +% +% COMMENTS: +% The model estimated is Y = X*B + epsilon where Var(epsilon)=S2 +% +% EXAMPLES: +% Estimate a regression with a constant +% b = ols(y,x) +% Estimate a regression without a constant +% b = ols(y,x,0) +% +% See also OLSNW + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + + +%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%% +if nargin<2 || nargin>3 + error('2 or 3 inputs only') +end +% Check y +if size(y,1)N + error('The number of columns of X must be grater than or equal to T') + end + if rank(x)1 +% A scalar GED r.v. with variance normalized to 1 has probability +% density given by: +% f(x,V) = [V/(lda*2^(1+1/V)*gamma(1/V))]*exp(-0.5*|x/lda|^V) +% lda = [2^(-2/V)*gamma(1/V)/gamma(3/V)]^0.5 +% Uses GAMCDF +% +% REFERENCES: +% [1] Tadikamalla (1980), J.Am.Stat.Assoc. (75) +% [2] Nelson (1991), Econometrica +% +% See also GEDPDF, GEDINV, GEDRND, GEDLOGLIK GAMCDF + +% Copyright: +% Ivana Komunjer +% komunjer@hss.caltech.edu +% Revision: 1 Date: 23/08/2002 +% Modifications Copyright: +% Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 8/1/2005 +if nargin~=2 + error('Requires two input arguments.') +end + +[err, errtext, sizeOut, v] = iscompatible(1,v,size(x)); + +if err + error(errtext) +end + +% Initialize P to zero. +p = zeros(size(x)); +scalex = (gamma(3./v)./gamma(1./v)).^0.5; + +% Return NaN if the argument V is outside its limits. +p(v < 1) = NaN; + +ku = find(x >= 0 & ~(v < 1)); +vku = v(ku); +xku = x(ku); +scalexku = scalex(ku); +if any(ku), + p(ku) = 0.5*(1 + gamcdf((abs(xku.*scalexku)).^vku,1./vku)); +end + +kl = find(x < 0 & ~(v < 1)); +vkl = v(kl); +xkl = x(kl); +scalexkl = scalex(kl); +if any(kl), + p(kl) = 0.5*(1 - gamcdf((abs(xkl.*scalexkl)).^vkl,1./vkl)); +end + +% Make sure that round-off errors never make P less than 0 or greater than 1. +p(p < 0) = 0; +p(p > 1) = 1; \ No newline at end of file diff --git a/distributions/gedinv.m b/distributions/gedinv.m new file mode 100644 index 0000000..44073c0 --- /dev/null +++ b/distributions/gedinv.m @@ -0,0 +1,90 @@ +function x = gedinv(p,v) +% Inverse Cumulative Distribution Function (CDF) of the Generalized Error +% distribution; Maps [0,1] to a standardized Students-t with V degrees of freedom +% +% USAGE: +% X = stdtinv(P,V) +% +% INPUTS: +% P - Values to be inverted, P in [0,1] +% V - Degree of freedom parameters, either scalar or size(X) +% +% OUTPUTS: +% X - Standardized T distributed random variables corresponding to P +% +% COMMENTS: +% A scalar GED r.v. with variance normalized to 1 has probability +% density given by: +% f(x,V) = [V/(lda*2^(1+1/V)*gamma(1/V))]*exp(-0.5*|x/lda|^V) +% lda = [2^(-2/V)*gamma(1/V)/gamma(3/V)]^0.5 +% GAMINV does the computational work +% +% REFERENCES: +% [1] Tadikamalla (1980), J.Am.Stat.Assoc. (75) +% [2] Nelson (1991), Econometrica +% +% See also STDTCDF, STDTINV, STDTRND, STDTLOGLIK, TPDF + +% Copyright: Ivana Komunjer +% komunjer@hss.caltech.edu +% Revision: 1 Date: 23/08/2002 +% Modifications Copyright: +% Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + +if nargin~=2 + error('Requires two input arguements.') +end + +[err, errtext, sizeOut, v] = iscompatible(1,v,size(p)); + +if err + error(errtext) +end + +% Initialize X to zero. +x = zeros(size(p)); +scalex = (gamma(3./v)./gamma(1./v)).^0.5; + +k = find(p<0 | p>1 | v < 1); +if any(k), + tmp = NaN; + x(k) = tmp(ones(size(k))); +end + +% The inverse cdf of 0 is 0, and the inverse cdf of 1 is 1. +k0 = find(p == 0 & v >= 1); +if any(k0), + x(k0) = zeros(size(k0)); +end + +k1 = find(p == 1 & v >= 1); +if any(k1), + tmp = Inf; + x(k1) = tmp(ones(size(k1))); +end + +% Tadikamalla's Method: uses the fact that Y=abs(X)^v has +% a Gamma distribution with shape parameter 1/v +kl = find(p > 0 & p < 0.5 & v >= 1); +if any(kl(:)) + pkl = p(kl); + vkl = v(kl); + xkl = gaminv(1-2*pkl,1./vkl); + xkl = (-1)*xkl.^(1./vkl); + x(kl) = xkl; +end + +ku = find(p >= 0.5 & p < 1 & v >= 1); +if any(ku(:)) + pku = p(ku); + vku = v(ku); + xku = gaminv(2*pku-1,1./vku); + xku = xku.^(1./vku); + x(ku) = xku; +end + +% need to standardize the quantiles +x = x./scalex; + diff --git a/distributions/gedloglik.m b/distributions/gedloglik.m new file mode 100644 index 0000000..7c14a10 --- /dev/null +++ b/distributions/gedloglik.m @@ -0,0 +1,74 @@ +function [LL,LLS]=gedloglik(x,mu,sigma2,v) +% Log likelihood for the Generalized Error Distribution (GED) distribution +% +% USAGE: +% [LL,LLS]=gedloglik(X,MU,SIGMA2,V) +% +% INPUTS: +% X - Standardized T random variables, either scalar or column vector +% MU - Mean of X, either scalar or size(x) +% SIGMA2 - Variance of X, either scalar or size(x) +% V - Degree of freedom parameters, either scalar or size(x) +% +% OUTPUTS: +% LL - Log-likelihood evaluated at X +% LLS - Vector of log-likelihoods corresponding to X +% +% COMMENTS: +% V>1 +% f(x,V) = [v/(lda*2^(1+1/v)*gamma(1/v))]*exp(-0.5*|x/lda|^v) +% lda = [2^(-2/v)*gamma(1/v)/gamma(3/v)]^0.5 +% +% REFERENCES: +% [1] Tadikamalla (1980), J.Am.Stat.Assoc. (75) +% [2] Nelson (1991), Econometrica +% +% See also GEDCDF, GEDINV, GEDRND, GEDPDF + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 9/1/2005 + +[T,K]=size(x); + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if K~=1 + error('X must be a column vector'); +end + +if nargin==4 + if length(mu)~=1 && ~all(size(mu)==[T K]) + error('mu must be either a scalar or the same size as X'); + end + if any(sigma2<=0) + error('sigma2 must contain only positive elements') + end + if length(sigma2)==1 + sigma2=sigma2*ones(T,K); + elseif size(sigma2,1)~=T || size(sigma2,2)~=1 + error('sigma2 must be a scalar or a vector with the same dimensions as X'); + end + if length(v)>1 || v<=1 + error('V must be a scalar greater than 1'); + end + x=x-mu; +else + error('Only 4 inputs supported'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%Compute the log likelihood +logl=0.5*(-2/v*log(2)+gammaln(1/v)-gammaln(3/v)); +l=exp(logl); +LL = (T * log(v)) - (T*logl) - (T*gammaln(1/v)) - T*(1+1/v)*log(2); +LL = LL - 0.5 * sum(log(sigma2)) - 0.5 * sum((abs(x./(sqrt(sigma2)*l))).^v); + +%Compute the individual LLS if needed +if nargout>1 + LLS = log(v) - logl - gammaln(1/v) - (1+1/v)*log(2) - 0.5 * log(sigma2) - 0.5 * (abs(x./(sqrt(sigma2)*l))).^v; + % LLS=log(v)-logl-0.5*abs(x./l).^v-logl-(1+1/v)*log(2)-gammaln(1/v); +end diff --git a/distributions/gedpdf.m b/distributions/gedpdf.m new file mode 100644 index 0000000..3acec17 --- /dev/null +++ b/distributions/gedpdf.m @@ -0,0 +1,56 @@ +function y = gedpdf(x,v) +% Probability Density Function (PDF) for the Generalized Error Distribution (GED) +% +% USAGE: +% Y = gedpdf(X,V) +% +% INPUTS: +% X - Generalized Error Distribution distributed random variables +% V - Degree of freedom parameters, either scalar or size(x) +% +% OUTPUTS: +% Y - Probability density evaluated at x +% +% COMMENTS: +% V>=1 +% A scalar GED r.v. with variance normalized to 1 has probability +% density given by: +% f(x,V) = [V/(lda*2^(1+1/V)*gamma(1/V))]*exp(-0.5*|x/lda|^V) +% lda = [2^(-2/V)*gamma(1/V)/gamma(3/V)]^0.5 +% +% REFERENCES: +% [1] Tadikamalla (1980), J.Am.Stat.Assoc. (75) +% [2] Nelson (1991), Econometrica +% +% See also GEDCDF, GEDINV, GEDRND, GEDLOGLIK + +% Copyright: Ivana Komunjer +% komunjer@hss.caltech.edu +% Revision: 1 Date: 23/08/2002 +% Modifications Copyright: +% Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 8/1/2005 + +if nargin~=2 + error('Requires two input arguments.') +end + +[err, errtext, sizeOut, v] = iscompatible(1,v,size(x)); + +if err + error(errtext) +end + +% Initialize D to zero. +y = zeros(size(x)); + +% Return NaN if the argument V is outside its limit. +y(v < 1) = NaN; + +k = find(v >= 1); +vk = v(k); xk = x(k); +if any(k) + ldak = ((2.^(-2./vk)).*(gamma(1./vk))./(gamma(3./vk))).^(0.5); + y(k) = vk.*exp(-0.5*((abs(xk./ldak)).^vk))./(ldak.*gamma(1./vk).*(2.^(1+1./vk))); +end \ No newline at end of file diff --git a/distributions/gedrnd.m b/distributions/gedrnd.m new file mode 100644 index 0000000..f7e2bed --- /dev/null +++ b/distributions/gedrnd.m @@ -0,0 +1,64 @@ +function r = gedrnd(v,varargin) +% Generate random variables from a Generalized Error Distribution (GED) with V degrees of freedom +% +% USAGE: +% R=gedrnd(V) +% R=gedrnd(V,S1) +% R=gedrnd(V,S1,S2,S3,...,SN) +% R=gedrnd(V,[S1 S2 S3 ... SN]) +% +% INPUTS: +% V - Degree of freedom parameter. Either scalar or matrix. +% Sx - [OPTIONAL] Size of output. +% R will be: +% 1 by 1 if V is scalar and no S are entered +% size(V) if V is non-scalar and no S are entered +% S1 by S1 if V is scalar and only S1 is entered +% [S1 S2 ... SN] otherwise +% If V is non-scalar and S are provided, size(V) must equal [S1 S2 ... SN] +% +% OUTPUTS: +% R - GED distributed random variables +% +% COMMENTS: +% V>=1 +% A scalar GED r.v. with variance normalized to 1 has probability +% density given by: +% f(x,v) = [v/(lda*2^(1+1/v)*gamma(1/v))]*exp(-0.5*|x/lda|^v) +% lda = [2^(-2/v)*gamma(1/v)/gamma(3/v)]^0.5 +% If X~GED(v) then abs(X)^v = Y~Gamma(1/v) (cf. Tadikamalla 1980). +% GAMRND does the computational work. +% +% REFERENCES: +% [1] Tadikamalla (1980), J.Am.Stat.Assoc. (75) +% [2] Nelson (1991), Econometrica +% +% See also GEDPDF, GEDCDF, GEDINV, GEDLL, GAMRND + +% Copyright: Ivana Komunjer +% komunjer@hss.caltech.edu +% Modifications Copyright: +% Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + +if nargin < 1, + error('Requires at least one input argument.'); +end + +v(v<1)=NaN; + +[err, errtext, sizeOut] = iscompatible(1,v,varargin{:}); + +if err + error(errtext) +end + +% Return NaN if the argument V is outside its limit. +r = gamrnd(1./v,1,sizeOut); +r = r.^(1./v); +rndsgn = 2*((rand(sizeOut)>0.5)-0.5); % generates a random sign -1 or +1 +r = r.*rndsgn; + +scalex = (gamma(3./v)./gamma(1./v)).^0.5; % standardizes the obtained values +r = r./scalex; \ No newline at end of file diff --git a/distributions/mvnormloglik.m b/distributions/mvnormloglik.m new file mode 100644 index 0000000..5fd0ed6 --- /dev/null +++ b/distributions/mvnormloglik.m @@ -0,0 +1,102 @@ +function [LL,lls]=mvnormloglik(x,mu,sigma) +% Log-likelihood for the multivariate normal distribution +% +% USAGE: +% [LL,LLS]=mvnormloglik(X,MU,SIGMA) +% +% INPUTS: +% X - Normal random variables, T by K +% MU - Mean of X, either K by 1 or T by K +% SIGMA - Covariance of X, either K by K or K by K by T +% +% OUTPUTS: +% LL - Log-likelihood evaluated at X +% LLS - Vector of log-likelihoods corresponding to X +% +% COMMENTS: +% +% REFERENCES: +% [1] Cassella and Berger (1990) 'Statistical Interence' +% +% See also NORMLOGLIK + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 2/1/2007 + +[T,K]=size(x); + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if ndims(x)>2 + error('X must be a T by K matrix'); +end + +if nargin==1 + sigma = eye(K); + sigma_is_2D=true; +elseif nargin==2 + %Check mu's conformability + if ndims(mu)>2 || ~(all(size(mu)==[K 1]) || all(size(mu)==[T K])) + error('MU must be either a K by 1 vector or the same size as X'); + end + if size(mu,1)==K + mu=repmat(mu',T,1); + end + x=x-mu; + sigma=eye(K); + sigma_is_2D=true; +elseif nargin==3 + if ndims(mu)>2 || ~(all(size(mu)==[K 1]) || all(size(mu)==[T K])) + error('MU must be either a K by 1 vector or the same size as X'); + end + if size(mu,1)==K + mu=repmat(mu',T,1); + end + x=x-mu; + switch ndims(sigma) + case 2 + % Must by K by K and PD + if size(sigma,1)~=K || size(sigma,2)~=K || min(eig(sigma))<=0 || any(any(sigma~=sigma')) + error('SIGMA must by either K by K and positive definite, or K by K by T and contain only positive definite matrices.') + end + sigma_is_2D=true; + case 3 + if size(sigma,1)~=K || size(sigma,2)~=K || size(sigma,3)~=T + error('SIGMA must by either K by K and positive definite, or K by K by T and contain only positive definite matrices.') + end + for t=1:T + s=sigma(:,:,t); + if min(eig(s)<=0) || any(any(s~=s')) + error('SIGMA must by either K by K and positive definite, or K by K by T and contain only positive definite matrices.') + end + end + sigma_is_2D=false; + otherwise + error('SIGMA must by either K by K and positive definite, or K by K by T and contain only positive definite matrices.') + end +else + error('Only 1 to 3 inputs supported'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%Compute the log likelihood +if sigma_is_2D + stdx=x*sigma^(-0.5); + LL = -0.5 * (T*K*log(2*pi) + T*log(det(sigma)) + sum(sum(stdx.^2))); + %Compute the individual log likelihoods if needed + if nargout>1 + lls = -0.5*(K*log(2*pi) + log(det(sigma)) + sum(stdx.^2,2)); + end +else + lls=zeros(T,1); + for t=1:T + s=sigma(:,:,t); + lls(t) = -0.5*(K*log(2*pi) + log(det(s)) + x(t,:)*inv(s)*x(t,:)'); + end + LL=sum(lls); +end + diff --git a/distributions/normloglik.m b/distributions/normloglik.m new file mode 100644 index 0000000..c9bf11f --- /dev/null +++ b/distributions/normloglik.m @@ -0,0 +1,74 @@ +function [LL,lls]=normloglik(x,mu,sigma2) +% Log-likelihood for the normal distribution +% +% USAGE: +% [LL,LLS]=normloglik(X,MU,SIGMA2) +% +% INPUTS: +% X - Normal random variables, either scalar or column vector +% MU - Mean of X, either scalar or size(x) +% SIGMA2 - Variance of X, either scalar or size(x) +% +% OUTPUTS: +% LL - Log-likelihood evaluated at X +% LLS - Vector of log-likelihoods corresponding to X +% +% COMMENTS: +% +% REFERENCES: +% [1] Cassella and Berger (1990) 'Statistical Interence' +% +% See also NORMCDF, NORMINV, NORMRND, NORMPDF + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 9/1/2005 + +[T,K]=size(x); + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if K~=1 + error('x must be a column vector'); +end + +if nargin==1 + sigma2=ones(T,K); +elseif nargin==2 + %Check mu's conformability + if length(mu)~=1 && ~all(size(mu)==[T K]) + error('mu must be either a scalar or the same size as X'); + end + x=x-mu; + sigma2=ones(T,K); +elseif nargin==3 + if length(mu)~=1 && ~all(size(mu)==[T K]) + error('mu must be either a scalar or the same size as X'); + end + if any(sigma2<=0) + error('sigma2 must contain only positive elements') + end + if length(sigma2)==1 + sigma2=sigma2*ones(T,K); + elseif size(sigma2,1)~=T || size(sigma2,2)~=1 + error('sigma2 must be a scalar or a vector with the same dimensions as x'); + end + x=x-mu; +else + error('Only 1 to 3 inputs supported'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +if nargout>1 +%Compute the individual log likelihoods if needed + lls = -0.5*(log(2*pi) + log(sigma2) + x.^2./sigma2); + % Use these to comput the LL + LL = sum(lls); +else + %Compute the log likelihood + LL = -0.5 * (sum(log(sigma2)) + sum((x.^2)./sigma2) + T*log(2*pi)); +end diff --git a/distributions/skewtcdf.m b/distributions/skewtcdf.m new file mode 100644 index 0000000..ccff810 --- /dev/null +++ b/distributions/skewtcdf.m @@ -0,0 +1,59 @@ +function p = skewtcdf(x,v,lambda) +% Cumulative Distribution Function (CDF) of Hansen's (1994) Skewed T distribution +% +% USAGE: +% P = skewtcdf(X,V,LAMBDA) +% +% INPUTS: +% X - Standardized T random variables +% V - Degree of freedom parameters, either scalar or size(X) +% LAMBDA - Asymmetry Parameter +% +% OUTPUTS: +% P - Cumulative distribution evaluated at x +% +% COMMENTS: +% V>2 +% -1=-a./b).*((1-lambda)/2 + (1+lambda).*(tcdf(y2,v)-0.5)); + +%Original Nonvector code +%cdf = -999.99*ones(T,1); +%for tt = 1:T; +% if x(tt)<(-a(tt)/b(tt)) +% cdf(tt) = (1-lambda(tt)).*tdis_cdf(y1(tt),v(tt)); +% else +% cdf(tt) = ((1-lambda(tt))/2 + (1+lambda(tt)).*(tdis_cdf(y2(tt),v(tt))-0.5)); +% end +%end \ No newline at end of file diff --git a/distributions/skewtinv.m b/distributions/skewtinv.m new file mode 100644 index 0000000..9b46f75 --- /dev/null +++ b/distributions/skewtinv.m @@ -0,0 +1,55 @@ +function x=skewtinv(p,v,lambda) +% Inverse Cumulative Distribution Function (CDF) of Hansen's (1994) 'skewed t' +% distribution; Maps [0,1] to a Skewed-t with V degrees of freedom, shape LAMBDA +% +% USAGE: +% X=skewtinv(P,V,LAMBDA) +% +% INPUTS: +% P - Values to be inverted, P in [0,1] +% V - Degree of freedom parameters, either scalar or size(X) +% LAMBDA - Degree of freedom parameters, either scalar or size(X) +% +% OUTPUTS: +% X - Skewed T distributed random variables corresponding to P +% +% COMMENTS: +% V>2 +% -.99.99)=NaN; + +c = gamma((v+1)/2)./(sqrt(pi*(v-2)).*gamma(v/2)); +a = 4*lambda.*c.*((v-2)./(v-1)); +b = sqrt(1 + 3*lambda.^2 - a.^2); + +f1 = find(p<((1-lambda)/2)); +f2 = find(p>=((1-lambda)/2)); + +inv1 = (1-lambda(f1))./b(f1).*sqrt((v(f1)-2)./v(f1)).*tinv(p(f1)./(1-lambda(f1)),v(f1))-a(f1)./b(f1); +inv2 = (1+lambda(f2))./b(f2).*sqrt((v(f2)-2)./v(f2)).*tinv(0.5+1./(1+lambda(f2)).*(p(f2)-(1-lambda(f2))./2),v(f2))-a(f2)./b(f2); +x = repmat(NaN,sizeOut); +x(f1) = inv1; +x(f2) = inv2; \ No newline at end of file diff --git a/distributions/skewtloglik.m b/distributions/skewtloglik.m new file mode 100644 index 0000000..1d7bed4 --- /dev/null +++ b/distributions/skewtloglik.m @@ -0,0 +1,86 @@ +function [LL,LLS]=skewtloglik(x,mu,sigma2,v,lambda) +% Log likelihood for Hansen's Skewed T distribution +% +% USAGE: +% [LL,LLS]=skewtloglik(X,MU,SIGMA2,V,LAMBDA) +% +% INPUTS: +% X - Standardized T random variables, either scalar or column vector +% MU - Mean of X, either scalar or size(x) +% SIGMA2 - Variance of X, either scalar or size(x) +% V - Degree of freedom parameters, either scalar or size(x) +% LAMBDA - Asymmetry parameter +% +% OUTPUTS: +% LL - Log-likelihood evaluated at X +% LLS - Vector of log-likelihoods corresponding to X +% +% COMMENTS: +% V>2, -11 || v<=2 + error('V must be a scalar greater than 2'); + end + if length(lambda)>1 || lambda<=-1 || lambda>=1 + error('LAMBDA must be a scalar between -1 and 1'); + end + x=x-mu; +else + error('Only 5 inputs supported'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%Compute the log likelihood +logc = gammaln((v+1)/2) - gammaln(v/2) - 0.5*log(pi*(v-2)); +c = exp(logc); + +a = 4*lambda.*c.*((v-2)./(v-1)); +logb = 0.5*log(1 + 3*lambda.^2 - a.^2); +b = exp(logb); + +stdresid=x./sqrt(sigma2); + +find1 = (stdresid<(-a./b)); +find2 = (stdresid>=(-a./b)); +LL1 = logb + logc - (v+1)/2.*log(1+1./(v-2).*((b.*stdresid(find1)+a)./(1-lambda)).^2); +LL2 = logb + logc - (v+1)/2.*log(1+1./(v-2).*((b.*stdresid(find2)+a)./(1+lambda)).^2); +LL = sum(LL1) + sum(LL2) - 0.5*sum(log(sigma2)); + +%Compute the individual log likelihoods if needed +if nargout>1 + LLS=zeros(T,1); + LLS(find1)=LL1 - 0.5*log(sigma2(find1)); + LLS(find2)=LL2 - 0.5*log(sigma2(find2)); +end diff --git a/distributions/skewtpdf.m b/distributions/skewtpdf.m new file mode 100644 index 0000000..61f77a0 --- /dev/null +++ b/distributions/skewtpdf.m @@ -0,0 +1,50 @@ +function y = skewtpdf(x, v, lambda) +% Probability Density Function (PDF) of Hansen's (1994) Skewed T distribution +% +% USAGE: +% Y = skewtpdf(X,V,LAMBDA) +% +% INPUTS: +% X - Standardized T random variables +% V - Degree of freedom parameters, either scalar or size(x) +% LAMBDA - Asymmetry Parameter +% +% OUTPUTS: +% Y - Probability density evaluated at X +% +% COMMENTS: +% V>2 +% -11)=NaN; + +[err, errtext, sizeOut, v, lambda] = iscompatible(2,v,lambda,size(x)); + +if err + error(errtext) +end + +c = gamma((v+1)/2)./(sqrt(pi*(v-2)).*gamma(v/2)); +a = 4*lambda.*c.*((v-2)./(v-1)); +b = sqrt(1 + 3*lambda.^2 - a.^2); + +y1 = b.*c.*(1 + 1./(v-2).*((b.*x+a)./(1-lambda)).^2).^(-(v+1)/2); +y2 = b.*c.*(1 + 1./(v-2).*((b.*x+a)./(1+lambda)).^2).^(-(v+1)/2); +y = y1.*(x<(-a./b)) + y2.*(x>=(-a./b)); \ No newline at end of file diff --git a/distributions/skewtrnd.m b/distributions/skewtrnd.m new file mode 100644 index 0000000..482a233 --- /dev/null +++ b/distributions/skewtrnd.m @@ -0,0 +1,51 @@ +function r = skewtrnd(v,lambda,varargin) +% Generate random variables from Hansen's Skewed T distribution +% with V degrees of freedom and skewness parameter LAMBDA +% +% USAGE: +% R=skewtrnd(V,LAMBDA) +% R=skewtrnd(V,LAMBDA,S1) +% R=skewtrnd(V,LAMBDA,S1,S2,S3,...,SN) +% R=skewtrnd(V,LAMBDA,[S1 S2 S3 ... SN]) +% +% INPUTS: +% V - Degree of freedom parameter. Either scalar or matrix. +% LAMBDA - Skewness parameter +% Sx - [OPTIONAL] Size of output. +% R will be: +% 1 by 1 if V is scalar and no S are entered +% size(V) if V is non-scalar and no S are entered +% S1 by S1 if V is scalar and only S1 is entered +% [S1 S2 ... SN] otherwise +% If V is non-scalar and S are provided, size(V) must equal [S1 S2 ... SN] +% +% OUTPUTS: +% R - Skewed T distributed random variables +% +% COMMENTS: +% V>2 +% -.992 +% Uses TCDF +% +% REFERENCES: +% [1] Cassella and Berger (1990) 'Statistical Inference' +% +% See also STDTPDF, STDTINV, STDTRND, STDTLOGLIK, TCDF + +% Copyright: +% Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 8/1/2005 + +if nargin~=2 + error('2 inputs required') +end + +[err, errtext, sizeOut, v] = iscompatible(1,v,size(x)); +if err + error(errtext) +end + +%Compute the st +stdev=sqrt(v./(v-2)); +stdev(v<=2)=NaN; +x=x.*stdev; + +p=tcdf(x,v); diff --git a/distributions/stdtinv.m b/distributions/stdtinv.m new file mode 100644 index 0000000..9131120 --- /dev/null +++ b/distributions/stdtinv.m @@ -0,0 +1,42 @@ +function x=stdtinv(p,v) +% Inverse Cumulative Distribution Function (CDF) of the Standardized T +% distribution; Maps [0,1] to a standardized Students-t with V degrees of freedom +% +% USAGE: +% X = stdtinv(P,V) +% +% INPUTS: +% P - Values to be inverted, P in [0,1] +% V - Degree of freedom parameters, either scalar or size(X) +% +% OUTPUTS: +% X - Standardized T distributed random variables corresponding to P +% +% COMMENTS: +% V>2 +% +% REFERENCES: +% [1] Cassella and Berger (1990) 'Statistical Interence' +% +% See also STDTCDF, STDTINV, STDTRND, STDTLOGLIK, TPDF + +% Copyright: +% Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + + +if nargin~=2 + error('2 inputs required') +end + +[err, errtext, sizeOut, v] = iscompatible(1,v,size(p)); +if err + error(errtext) +end + +x=tinv(p,v); + +stdev=sqrt(v./(v-2)); +stdev(v<=2)=NaN; +x=x./stdev; \ No newline at end of file diff --git a/distributions/stdtloglik.m b/distributions/stdtloglik.m new file mode 100644 index 0000000..43b7d9c --- /dev/null +++ b/distributions/stdtloglik.m @@ -0,0 +1,70 @@ +function [ll,lls]=stdtloglik(x,mu,sigma2,nu) +% Log likelihood of the Standardized T distribution +% +% USAGE: +% [LL,LLS]=stdtloglik(X,MU,SIGMA2,NU) +% +% INPUTS: +% X - Standardized T random variables, either scalar or column vector +% MU - Mean of X, either scalar or size(x) +% SIGMA2 - Variance of X, either scalar or size(x) +% V - Degree of freedom parameters, either scalar or size(x) +% +% OUTPUTS: +% LL - Log-likelihood evaluated at X +% LLS - Vector of log-likelihoods corresponding to X +% +% COMMENTS: +% V>2 +% +% REFERENCES: +% [1] Cassella and Berger (1990) 'Statistical Inference' +% +% See also STDTCDF, STDTINV, STDTRND, STDTPDF + +% Copyright: +% Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 9/1/2004 + +[T,K]=size(x); + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if K~=1 + error('X must be a column vector'); +end + +if nargin==4 + if length(mu)~=1 && ~all(size(mu)==[T K]) + error('mu must be either a scalar or the same size as X'); + end + if any(sigma2<=0) + error('sigma2 must contain only positive elements') + end + if length(sigma2)==1 + sigma2=sigma2*ones(T,K); + elseif size(sigma2,1)~=T || size(sigma2,2)~=1 + error('sigma2 must be a scalar or a vector with the same dimensions as X'); + end + if length(nu)>1 || nu<=2 + error('nu must be a scalar greater than 2'); + end + x=x-mu; +else + error('Only 4 inputs supported'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%Compute the log likelihood +ll = T*gammaln(0.5*(nu+1)) - T*gammaln(nu/2) - T/2*log(pi*(nu-2)) ... + - 0.5*sum(log(sigma2)) - ((nu+1)/2)*sum(log(1 + (x.^2)./(sigma2*(nu-2)))); + +%Compute the individual log likelihoods if needed +if nargout>1 + lls = gammaln(0.5*(nu+1)) - gammaln(nu/2) - 1/2*log(pi*(nu-2))... + - 0.5*(log(sigma2)) - ((nu+1)/2)*(log(1 + (x.^2)./(sigma2*(nu-2)))); +end diff --git a/distributions/stdtpdf.m b/distributions/stdtpdf.m new file mode 100644 index 0000000..1cc9af6 --- /dev/null +++ b/distributions/stdtpdf.m @@ -0,0 +1,45 @@ +function y=stdtpdf(x,v) +% Probability Density Function (PDF) for the Standardized T distribution +% +% USAGE: +% Y = stdtpdf(X,V) +% +% INPUTS: +% X - Standardized T random variables +% V - Degree of freedom parameters, either scalar or size(x) +% +% OUTPUTS: +% Y - Probability density evaluated at x +% +% COMMENTS: +% V>2 +% Uses TPDF +% +% REFERENCES: +% [1] Cassella and Berger (1990) 'Statistical Inference' +% +% See also STDTCDF, STDTINV, STDTRND, STDTLOGLIK, TPDF + +% Copyright: +% Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 8/1/2005 + +% v must either be scalar or the same size as x +if nargin~=2 + error('2 inputs required') +end + +[err, errtext, sizeOut, v] = iscompatible(1,v,size(x)); + +if err + error(errtext) +end + +%stdev=sqrt(v./(v-2)); +%stdev(v<=2)=NaN; +%x=x.*stdev; + +constant = exp(gammaln((v+1)/2)-gammaln(v/2)); +y = constant./sqrt(pi*(v-2)).*(1+x.^2./(v-2)).^(-(v+1)/2); +%y=tpdf(x,v); \ No newline at end of file diff --git a/distributions/stdtrnd.m b/distributions/stdtrnd.m new file mode 100644 index 0000000..a23d58e --- /dev/null +++ b/distributions/stdtrnd.m @@ -0,0 +1,51 @@ +function r=stdtrnd(v,varargin) +% Generate random variables from a Standardized T distribution with V degrees of freedom +% +% USAGE: +% R=stdtrnd(V) +% R=stdtrnd(V,S1) +% R=stdtrnd(V,S1,S2,S3,...,SN) +% R=stdtrnd(V,[S1 S2 S3 ... SN]) +% +% INPUTS: +% V - Degree of freedom parameter. Either scalar or matrix. +% Sx - [OPTIONAL] Size of output. +% R will be: +% 1 by 1 if V is scalar and no S are entered +% size(V) if V is non-scalar and no S are entered +% S1 by S1 if V is scalar and only S1 is entered +% [S1 S2 ... SN] otherwise +% If V is non-scalar and S are provided, size(V) must equal [S1 S2 ... 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+if err + error(errtext) +end + +%Compute the st +p=repmat(NaN,sizeOut); +pl = v>0; +temp=gammainc(x(pl)/2,v(pl)*0.5); +p(pl)=temp; diff --git a/duplication/iscompatible.m b/duplication/iscompatible.m new file mode 100644 index 0000000..840a654 --- /dev/null +++ b/duplication/iscompatible.m @@ -0,0 +1,145 @@ +function [error, errortext, sizeOut, varargout]=iscompatible(narg,varargin) +% Check whether a set of input parameters is compatible with a requested output size +% +% USAGE: +% [ERROR, ERRORTEXT, SIZEOUT] = iscompatible(NARG,P1,P2,...,PK,S1,S2,...,SN) +% [ERROR, ERRORTEXT, SIZEOUT] = iscompatible(NARG,P1,P2,...,PK,[S1 S2 ... SN]) +% [ERROR, ERRORTEXT, SIZEOUT, P1, P2, ... , PK] = iscompatible(NARG,P1,P2,...,PK,S1,S2,...,SN) +% [ERROR, ERRORTEXT, SIZEOUT, P1, P2, ... , PK] = iscompatible(NARG,P1,P2,...,PK,[S1 S2 ... SN]) +% +% INPUTS: +% NARG - Number of parameters to be checked, K above +% Px - Parameters to be chekced. Must be as many as narg. May be +% either scalars of arrays +% Sx - Requested output size. Either individual scalars or a vector +% +% OUTPUTS: +% ERROR - 1 if there is a problem with the input parameters, 0 otherwise +% ERRORTEXT - A message detailing the nature of the problem +% SIZEOUT - The matched output size +% Px - Parameters transformed to all have the same dimension so that size(Px)=SIZEOUT +% +% COMMENTS: +% Helper function for various distribution, probability, inverse +% distribution and random number generators + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + +% General Strategy +% 1. Sort the parametes form the size arguements +% 2. Find max dim of parameters, make sure all are either 1 by 1 or this +% size; be careful if ndim is 2, then you want the max length +% 3. Figure out the output size, either a vector or a buch of scalars +% 4. Finally compare the parameter size to the SIZEOUT +% 5. Repmat the parameters is necessary + +% Default error text +errortext=''; +varargout=cell(narg); + +% Error if there are not enough inputs +if length(varargin)1)==1 + % If only one is non-scalar, it's size becomes the common size + param_size=size(params{param_len>1}); + +else + % If more than one are scalar, get all teh sizes and make sure they are + % the same + param_non_scalar=find(param_len>1); + params_non_scalar=params(param_non_scalar); + for i=1:size(params_non_scalar)-1 + % This is an error if any two non-scalar parameters have different + % sizes + if ~isequal(size(params_non_scalar{i}),size(params_non_scalar{i+1})) + sizeOut=[]; + error=1; + errortext='Parameter size mismatch. Must be either scalar or of a common size.'; + return + end + end + %If they all have the same size, then the parameter size is just hte + %size of the first non-scalar parameter + param_size=size(params_non_scalar{1}); +end + + +% Parse the requested output size +if length(varargin)>narg + sizeOut=varargin(narg+1:length(varargin)); + if length(sizeOut)==1 + sizeOut=sizeOut{1}; + if ndims(sizeOut)==2 && length(sizeOut)==numel(sizeOut) + else + sizeOut=[]; + error=1; + errortext=['Requested output size cannot be parsed. Should be a ' ... + 'vector or series of scalars.']; + return + end + else + if all(cellfun('length',sizeOut)==1) + sizeOut=cell2mat(sizeOut); + else + sizeOut=[]; + error=1; + errortext=['Requested output size cannot be parsed. Should be a ' ... + 'vector or series of scalars.']; + return + end + end +else + sizeOut=[]; +end + + + +% Finally, compare the parameter size to the requested output size +if prod(param_size)~=1 && ~isempty(sizeOut) + if isequal(param_size,sizeOut) + % If both are provided, are they equal + error=0; + else + % If not, an error + error=1; + sizeOut=[]; + errortext='Requested output size and parameters are not of compatible sizes.'; + return + end +elseif isempty(sizeOut) + % If no sizeOut is requested, then the parameter size is the sizeOut + sizeOut=param_size; + error=0; +else + % If all parameters are scalars, then and a sizeOut is provided, use that + error=0; +end + +% If the user wants transformed parameters to the common size, provide them +if nargout>3 + for i=1:narg; + if length(varargin{i})==1 + varargout{i}=repmat(varargin{i},sizeOut); + else + varargout{i}=varargin{i}; + end + end +end \ No newline at end of file diff --git a/duplication/kurtosis.m b/duplication/kurtosis.m new file mode 100644 index 0000000..6ff9054 --- /dev/null +++ b/duplication/kurtosis.m @@ -0,0 +1,27 @@ +function k=kurtosis(x, flag, dim) +% Estimate the 4th standardized moment from a vector or matix of data. +% +% K=kurtosis(X,FLAG,DIM) +% +% INPUTS +% X - Data to be used in skewness calculation +% FLAG - Not implemented +% DIM - Dimension to compute the kurtosis on if x is not a vector + +% Author: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 2/25/2006 + +if nargin==1 + dim=1; +end + +ncm1 = mean(x,dim); +ncm2 = mean(x.^2,dim); +ncm3 = mean(x.^3,dim); +ncm4 = mean(x.^4,dim); + +cm2 = ncm2-ncm1.^2; +cm4 = ncm4 - 4*ncm3.*ncm1 + 6*ncm1.^2.*ncm2 - 4.*ncm1.^4 + ncm1.^4; + +k = cm4./cm2.^2; diff --git a/duplication/normcdf.m b/duplication/normcdf.m new file mode 100644 index 0000000..79c8fdc --- /dev/null +++ b/duplication/normcdf.m @@ -0,0 +1,49 @@ +function p = normcdf(x,mu,sigma) +% Cumulative Distribution Function (CDF) of the Normal Distribution (Gaussian) +% +% USAGE: +% P = normcdf(X,MU,SIGMA) +% +% INPUTS: +% X - Normally distributed random variables +% MU - Mean parameter +% SIGMA - Standard deviation parameter +% +% OUTPUTS: +% P - Cumulative distribution evaluated at x +% +% COMMENTS: +% SIGMA>0 +% +% Uses ERFC +% +% See also NORMPDF, NORMINV, NORMRND, NORMLOGLIK + +%%%%%%%%%%%%%%%%% +% Error Checking +%%%%%%%%%%%%%%%%% +if nargin==1 + mu=0; + sigma=1; +elseif nargin==2 + sigma=1; +elseif nargin<1 || nargin>3 + error('Requires one to three input arguments.') +end + +[err, errtext, sizeOut, mu, sigma] = iscompatible(2,mu,sigma,size(x)); + +if err + error(errtext); +end +%%%%%%%%%%%%%%%%% +% Error Checking +%%%%%%%%%%%%%%%%% + + +% Initialize P to zero. +e = (x-mu)./sigma; +% Find any nan values +good = sigma>0; +p=repmat(NaN,size(x)); +p(good)=1-erfc(e(good)./sqrt(2))/2; \ No newline at end of file diff --git a/duplication/norminv.m b/duplication/norminv.m new file mode 100644 index 0000000..4120db0 --- /dev/null +++ b/duplication/norminv.m @@ -0,0 +1,49 @@ +function x = norminv(p,mu,sigma) +% Inverse Cumulative Distribution Function (CDF) of the Normal Distribution (Gaussian) +% +% USAGE: +% X = normcdf(P,MU,SIGMA) +% +% INPUTS: +% P - Cumulative distribution values +% MU - Mean parameter +% SIGMA - Standard deviation parameter +% +% OUTPUTS: +% X - Normally distributed random variables +% +% COMMENTS: +% SIGMA>0 +% +% Uses ERFINV +% +% See also NORMPDF, NORMINV, NORMRND, NORMLOGLIK + +%%%%%%%%%%%%%%%%% +% Error Checking +%%%%%%%%%%%%%%%%% +if nargin==1 + mu=0; + sigma=1; +elseif nargin==2 + sigma=1; +elseif nargin<1 || nargin>3 + error('Requires one to three input arguments.') +end + +[err, errtext, sizeOut, mu, sigma] = iscompatible(2,mu,sigma,size(p)); + +if err + error(errtext); +end +%%%%%%%%%%%%%%%%% +% Error Checking +%%%%%%%%%%%%%%%%% + +% Find any nan values +good = sigma>0 & p>=0 & p<=1; +x=repmat(NaN,size(p)); +x(p==.5)=0; +x(good & p>.5) = erfinv(2*(p(good & p>.5)-0.5))*sqrt(2); +x(good & p<.5) = -erfinv(2*(-p(good & p<.5)+0.5))*sqrt(2); +x=x.*sigma+mu; \ No newline at end of file diff --git a/duplication/normpdf.m b/duplication/normpdf.m new file mode 100644 index 0000000..6f672b0 --- /dev/null +++ b/duplication/normpdf.m @@ -0,0 +1,51 @@ +function y = normpdf(x,mu,sigma) +% Probability Density Function (PDF) of the Normal Distribution (Gaussian) +% +% USAGE: +% Y = normpdf(X,MU,SIGMA) +% +% INPUTS: +% X - Normally distributed random variables +% MU - Mean parameter +% SIGMA - Standard deviation parameter +% +% OUTPUTS: +% Y - Probability density evaluated at x +% +% COMMENTS: +% SIGMA>0 +% +% This is a clean room implementation that mimics the core function of +% MATLAB's normpdf. +% +% +% +% See also NORMPDF, NORMINV, NORMRND, NORMLOGLIK + +%%%%%%%%%%%%%%%%% +% Error Checking +%%%%%%%%%%%%%%%%% +if nargin==1 + mu=0; + sigma=1; +elseif nargin==2 + sigma=1; +elseif nargin<1 || nargin>3 + error('Requires one to three input arguments.') +end + +[err, errtext, sizeOut, mu, sigma] = iscompatible(2,mu,sigma,size(x)); + +if err + error(errtext); +end +%%%%%%%%%%%%%%%%% +% Error Checking +%%%%%%%%%%%%%%%%% + + +% Initialize y to nan. +% Find any nan values +good = sigma>0; +y=repmat(NaN,size(x)); +y(good)=(1./(sqrt(2*pi)*sigma)).*exp(-(x(good)-mu(good)).^2./(2*sigma(good).^2)); diff --git a/duplication/skewness.m b/duplication/skewness.m new file mode 100644 index 0000000..295070d --- /dev/null +++ b/duplication/skewness.m @@ -0,0 +1,27 @@ +function sk=skewness(x, flag, dim) +% Computes the standardized 3rd moment +% +% USAGE +% SK=skewness(X,FLAG,DIM) +% +% INPUTS +% X - Data to be used in skewness calculation +% FLAG - Not implemented +% DIM - Dimension to compute the skewness on if x is not a vector + +% Author: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 2/25/2006 + +if nargin==1 + dim=1; +end + +ncm1 = mean(x,dim); +ncm2 = mean(x.^2,dim); +ncm3 = mean(x.^3,dim); + +cm2 = ncm2-ncm1.^2; +cm3 = ncm3 - 3*ncm1.*ncm2 + 2.*ncm1.^3; + +sk = cm3./cm2.^(1.5); diff --git a/mex_source/agarch_core.c b/mex_source/agarch_core.c new file mode 100644 index 0000000..d3c3680 --- /dev/null +++ b/mex_source/agarch_core.c @@ -0,0 +1,105 @@ +/* Change this to reflect the apropriate header file */ +#include +#include "mex.h" +#include "matrix.h" + +/* + * agarch_core.c - + * This is a helper function and is part of the UCSD_GARCH toolbox + * You can compile it and should work on any platform. + * + * Copyright: Kevin Sheppard + * kevin.sheppard@economics.ox.ac.uk + * Revision: 1 Date: 7/12/2009 + */ +void agarch_core(double *data, double *parameters, double *back_cast, int p, int q, int m, mwSize T, int model_type, double *ht, double *shock) { + + mwIndex i, j; + double gamma, gamma2; + gamma = parameters[p+1]; + gamma2 = gamma * gamma; + + if (model_type == 1) { + for (j=0; j1) + mexErrMsgTxt("One output only."); + + /* Get the scalar inputs */ + p = (int)mxGetScalar(prhs[3]); + q = (int)mxGetScalar(prhs[4]); + m = (int)mxGetScalar(prhs[5]); + T = (mwSize)mxGetScalar(prhs[6]); + model_type = (int)mxGetScalar(prhs[7]); + + /* Create a pointer to the input matrices . */ + data = mxGetPr(prhs[0]); + parameters = mxGetPr(prhs[1]); + back_cast = mxGetPr(prhs[2]); + + + /* Set the output pointer to the output matrix. */ + plhs[0] = mxCreateDoubleMatrix(T, 1, mxREAL); + pTemp[0] = mxCreateDoubleMatrix(T,1, mxREAL); + + /* Create a C pointer to a copy of the output matrix. */ + ht = mxGetPr(plhs[0]); + shock = mxGetPr(pTemp[0]); + + + /* Call the C subroutine. */ + agarch_core(data, parameters, back_cast, p, q, m, T, model_type, ht, shock); + + /* Clean up */ + mxDestroyArray(pTemp[0]); +} \ No newline at end of file diff --git a/mex_source/armaxerrors.c b/mex_source/armaxerrors.c new file mode 100644 index 0000000..5251522 --- /dev/null +++ b/mex_source/armaxerrors.c @@ -0,0 +1,110 @@ +/* Change this to reflect the apropriate header file */ +#include +#include +#include "mex.h" +#include "matrix.h" + + +/* + * armaxerrors.c - + * This is a helper function and is part of the UCSD_GARCH/MFE toolbox + * You should be able to compile it on any platform. + * + * Author: Kevin Sheppard + * kevin.sheppard@economics.ox.ac.uk + * Revision: 3 Date: 10/16/2009 + */ + +void armaxerror_core(double *parameters, double *p, double *q, int constant, int np, int nq, double *y, double *x, size_t m, size_t T, size_t k, double *sigma, double *e) { + + /* + * e = zeros(T,1); + * for t=m+1:T + * e(t) = y(t); + * if constant + * e(t) = e(t) - parameters(1); + * end + * for i=1:np + * e(t) = e(t) - parameters(constant+i)*y(t-p(i)); + * end + * for i=1:k + * e(t) = e(t) - parameters(constant+np+i)*x(t,i); + * end + * for i=1:nq + * e(t) = e(t) - parameters(constant+np+k+i)*e(t-q(i)); + * end + * end + */ + size_t t, offSet; + int i; + for (t = 0; t < m; t++) + { + e[t] = 0; + } + for (t = m; t < T; t++) + { + e[t] = y[t]; + if (constant) + { + e[t] -= parameters[0]; + } + for (i = 0; i < np; i++) + { + e[t] -= parameters[constant + i] * y[t - (int)p[i]]; + } + for (i = 0; i < k; i++) + { + offSet = T * i; + e[t] -= parameters[constant + np + i] * x[t + offSet]; + } + for (i = 0; i < nq; i++) + { + e[t] -= parameters[constant + np + k + i] * e[t - (int)q[i]]; + } + e[t] = e[t]/sigma[t]; + } +} + + +/* The gateway routine */ +void mexFunction( int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[] ) { + /* 0 1 2 3 4 5 6 + * armaxerrors(parameters,p,q,constant,y,x,m) + */ + double *parameters, *q, *p, *y, *x, *e, *sigma; + int constant, np, nq; + size_t T, m, k; + + /* Check for proper number of arguments. */ + if (nrhs!=8) + mexErrMsgTxt("Eight inputs required."); + if (nlhs!=1) + mexErrMsgTxt("One output only."); + + /* Get the scalar inputs */ + constant = (int)mxGetScalar(prhs[3]); + m = (size_t)mxGetScalar(prhs[6]); + + /* Create a pointer to the input matrices . */ + parameters = mxGetPr(prhs[0]); + p = mxGetPr(prhs[1]); + q = mxGetPr(prhs[2]); + y = mxGetPr(prhs[4]); + x = mxGetPr(prhs[5]); + sigma = mxGetPr(prhs[7]); + + /* Get the dimensions of the matrix regressand to make an output matrix. */ + T = mxGetM(prhs[4]); + k = mxGetN(prhs[5]); + np = (int)mxGetM(prhs[1]); + nq = (int)mxGetM(prhs[2]); + + /* Set the output pointer to the output matrix. */ + plhs[0] = mxCreateDoubleMatrix((mwSize)T, 1, mxREAL); + + /* Create a C pointer to a copy of the output matrix. */ + e = mxGetPr(plhs[0]); + + /* Call the C subroutine. */ + armaxerror_core(parameters, p, q, constant, np, nq, y, x, m, T, k, sigma, e); +} \ No newline at end of file diff --git a/mex_source/egarch_core.c b/mex_source/egarch_core.c new file mode 100644 index 0000000..63230af --- /dev/null +++ b/mex_source/egarch_core.c @@ -0,0 +1,120 @@ +/* Change this to reflect the apropriate header file */ +#include +#include +#include "mex.h" +#include "matrix.h" + +/* +* egarch_core.c - +* This is a helper function and is part of the UCSD_GARCH toolbox +* You can compile it and should work on any platform. +* +* Author: Kevin Sheppard +* kevin.sheppard@economics.ox.ac.uk +* Revision: 3 Date: 3/1/2005 +*/ +void egarch_core(double *data, double *parameters, double *back_cast, double *upper, int p, int o, int q, int m, mwSize T, double *ht, double *logHt, double *stdData, double *absStdData) +{ + mwIndex i; + int j; + double exp_back_cast, vol, subconst, eLB, hLB; + + exp_back_cast=exp(back_cast[0]); + subconst = 0.797884560802865; + for (j=0; jupper[0]) + { + if(mxIsInf(ht[i])) + { + ht[i] = upper[0]; + } + else + { + ht[i]= upper[0] + logHt[i]; + } + logHt[i] = log(upper[0]); + } + vol = sqrt(ht[i]); + stdData[i] = data[i]/vol; + absStdData[i] = fabs(stdData[i])-subconst; + } +} + + +/* The gateway routine */ +void mexFunction( int nlhs, mxArray *plhs[], + int nrhs, const mxArray *prhs[]) +{ + /*ht=egarch_core(data,parameters,back_cast,upper,p,o,q,m,T);*/ + double *data, *parameters, *ht, *back_cast, *upper, *logHt, *stdData, *absStdData; + int p, o, q, m; + mwSize T; + mxArray *pTemp[3]; + + /* Check for proper number of arguments. */ + if(nrhs!=9) + mexErrMsgTxt("Nine inputs required."); + if(nlhs>1) + mexErrMsgTxt("One output only."); + + /* Get the scalar inputs */ + p = (int)mxGetScalar(prhs[4]); + o = (int)mxGetScalar(prhs[5]); + q = (int)mxGetScalar(prhs[6]); + m = (int)mxGetScalar(prhs[7]); + T = (mwSize)mxGetScalar(prhs[8]); + + /* Create a pointer to the input matrices . */ + data = mxGetPr(prhs[0]); + parameters = mxGetPr(prhs[1]); + back_cast = mxGetPr(prhs[2]); + upper = mxGetPr(prhs[3]); + + + /* Set the output pointer to the output matrix. */ + plhs[0] = mxCreateDoubleMatrix(T,1, mxREAL); + pTemp[0] = mxCreateDoubleMatrix(T,1, mxREAL); + pTemp[1] = mxCreateDoubleMatrix(T,1, mxREAL); + pTemp[2] = mxCreateDoubleMatrix(T,1, mxREAL); + + /* Create a C pointer to a copy of the output matrix. */ + ht = mxGetPr(plhs[0]); + logHt = mxGetPr(pTemp[0]); + stdData = mxGetPr(pTemp[1]); + absStdData = mxGetPr(pTemp[2]); + + /* Call the C subroutine. */ + egarch_core(data, parameters, back_cast, upper, p, o, q, m, T, ht, logHt, stdData, absStdData); + mxDestroyArray(pTemp[0]); + mxDestroyArray(pTemp[1]); + mxDestroyArray(pTemp[2]); +} \ No newline at end of file diff --git a/mex_source/igarch_core.c b/mex_source/igarch_core.c new file mode 100644 index 0000000..d5d6b22 --- /dev/null +++ b/mex_source/igarch_core.c @@ -0,0 +1,84 @@ +/* Change this to reflect the apropriate header file */ +#include +#include "mex.h" +#include "matrix.h" + +/* + * igarch_core.c - + * This is a helper function and is part of the UCSD_GARCH toolbox + * You can compile it and should work on any platform. + * + * Copyright: Kevin Sheppard + * kevin.sheppard@economics.ox.ac.uk + * Revision: 3 Date: 9/1/2005 + */ +void igarch_core(double *fepsilon, double *parameters, double *backCast, int p, int q, int m, mwSize T, int igarchType, int constant, double *ht) { + mwIndex i, j; + + /* Initialize the final parameter */ + double finalParameter = 1; + for (i = 0; i < p + q -1; i++) { + finalParameter -= parameters[constant+i]; + } + + for (j=0; j1) + mexErrMsgTxt("One output only."); + + /* Get the scalar inputs */ + p = (int)mxGetScalar(prhs[3]); + q = (int)mxGetScalar(prhs[4]); + m = (int)mxGetScalar(prhs[5]); + T = (mwSize)mxGetScalar(prhs[6]); + igarchType = (int)mxGetScalar(prhs[7]); + constant = (int)mxGetScalar(prhs[8]); + + /* Create a pointer to the input matrices . */ + fepsilon = mxGetPr(prhs[0]); + parameters = mxGetPr(prhs[1]); + backCast = mxGetPr(prhs[2]); + + /* Set the output pointer to the output matrix. */ + plhs[0] = mxCreateDoubleMatrix(T, 1, mxREAL); + + /* Create a C pointer to a copy of the output matrix. */ + ht = mxGetPr(plhs[0]); + + /* Call the C subroutine. */ + igarch_core(fepsilon, parameters, backCast, p, q, m, T, igarchType, constant, ht); +} \ No newline at end of file diff --git a/mex_source/tarch_core.c b/mex_source/tarch_core.c new file mode 100644 index 0000000..50d5368 --- /dev/null +++ b/mex_source/tarch_core.c @@ -0,0 +1,85 @@ +/* Change this to reflect the apropriate header file */ +#include +#include "mex.h" +#include "matrix.h" + +/* +* tarch_core.c - +* This is a helper function and is part of the UCSD_GARCH toolbox +* You can compile it and should work on any platform. +* +* Copyright: Kevin Sheppard +* kevin.sheppard@economics.ox.ac.uk +* Revision: 3 Date: 9/1/2005 +*/ +void tarch_core(double *fdata, double *fIdata, double *parameters, double *back_cast, int p, int o, int q, int m, mwSize T, int tarch_type, double *ht) +{ + mwIndex i, j; + + for (j=0; j1) + mexErrMsgTxt("One output only."); + + /* Get the scalar inputs */ + p = (int)mxGetScalar(prhs[4]); + o = (int)mxGetScalar(prhs[5]); + q = (int)mxGetScalar(prhs[6]); + m = (int)mxGetScalar(prhs[7]); + T = (mwSize)mxGetScalar(prhs[8]); + tarch_type = (int)mxGetScalar(prhs[9]); + + /* Create a pointer to the input matrices . */ + fdata = mxGetPr(prhs[0]); + fIdata = mxGetPr(prhs[1]); + parameters = mxGetPr(prhs[2]); + back_cast = mxGetPr(prhs[3]); + + + /* Set the output pointer to the output matrix. */ + plhs[0] = mxCreateDoubleMatrix(T,1, mxREAL); + + /* Create a C pointer to a copy of the output matrix. */ + ht = mxGetPr(plhs[0]); + + /* Call the C subroutine. */ + tarch_core(fdata, fIdata, parameters, back_cast, p, o, q, m, T, tarch_type, ht); + +} \ No newline at end of file diff --git a/multivariate/ccc_mvgarch.m b/multivariate/ccc_mvgarch.m new file mode 100644 index 0000000..3a81e73 --- /dev/null +++ b/multivariate/ccc_mvgarch.m @@ -0,0 +1,242 @@ +function [parameters, ll, ht, VCV, scores] = ccc_mvgarch(data,dataAsym,p,o,q,startingVals,options) +% Estimation of TARCH(p,o,q) - Constant Conditional Correlation MV GARCH +% +% USAGE: +% [PARAMETERS,LL,HT,VCV,SCORES] = ccc_mvgarch(DATA,DATAASYM,P,O,Q,STARTINGVALS,OPTIONS) +% +% INPUTS: +% DATA - A T by K matrix of zero mean residuals -OR- +% K by K by T array of covariance estimators (e.g. realized covariance) +% DATAASYM - [OPTIONAL] +% P - Positive, scalar integer representing the number of symmetric innovations -OR- +% K by 1 vector of individual symmetric innovations order +% O - Non-negative, scalar integer representing the number of asymmetric lags -OR- +% K by 1 vector of individual asymmetric innovations order +% Q - Non-negative, scalar integer representing the number of conditional variance lags -OR- +% K by 1 vector of individual conditional variance lags +% STARTINGVALS - [OPTIONAL] Vector of starting values for the K TARCH models. It should have the +% form [tarch(1)' tarch(2)' ... tarch(k)'] +% where each set of TARCH parameters is +% tarch(i) = +% [omega(i) alpha(i,1) ... alpha(i,p(i)) gamma(i,1) +% ... gamma(i,o(i)) beta(i,1) ... beta(i,q(i))]' +% OPTIONS - [OPTIONAL] Options to use in the TARCH model optimization (fminunc) +% +% OUTPUTS: +% PARAMETERS - a parameter vector of the form +% [tarch(1)' tarch(2)' ... tarch(k)' corr_vech(R)] +% where each set of TARCH parameters is +% tarch(i) = +% [omega(i) alpha(i,1) ... alpha(i,p(i)) gamma(i,1) +% ... gamma(i,o(i)) beta(i,1) ... beta(i,q(i))]' +% and where R is the constant conditional correlation. +% LL - The log likelihood at the optimum +% HT - A [K K T] dimension matrix of conditional covariances +% VCV - A numParams^2 square matrix of robust parameter covariances (A^(-1)*B*A^(-1)*t^(-1)) +% SCORES - A T by numParams matrix of individual scores +% +% COMMENTS: +% The conditional variance, H(t), of a constant conditional correlation model is +% H(t) = Sigma(t) * R * Sigma(t) +% +% where Sigma(t) is a diagonal matrix with TARCH(P,O,Q) volatilities on its diagonal. + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 10/28/2009 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 5 + startingVals = []; + options = []; + case 6 + options = []; + case 7 + % Nothing + otherwise + error('Between 5 and 7 arguments required.') +end + +%data should be TxK, T>K +if ndims(data)==2 + [t,k]=size(data); + if ~isempty(dataAsym) + error('If DATA is a T by K matrix, DATAASYM must be empty.'); + end + temp = zeros(k,k,t); + dataAsym = zeros(k,k,t); + for i=1:t + temp(:,:,i) = data(i,:)'*data(i,:); + dataAsym(:,:,i) = (data(i,:).*(data(i,:)<0))'*(data(i,:).*(data(i,:)<0)); + end + data = temp; +elseif ndims(data)==3 + [k,m,t] = size(data); + if m~=k + error('DATA must be K by K by T is a 3D array.'); + end + if ~isempty(dataAsym) + if ndims(dataAsym)~=3 + error('DATAASYM must be a 3D array with the same dimensions as DATA'); + end + [k2,m2,t2]=size(dataAsym); + if any([k m t]~=[k2 m2 t2]) + error('DATAASYM must be a 3D array with the same dimensions as DATA'); + end + end +end + +if min(t,k)<2 || tK>1'); +end + +%p, o, q much be non-negative scalars +% p +if length(p)==1 + if p<1 || floor(p)~=p + error('P must be a positive integer if scalar.'); + end + p = ones(k,1) * p; +else + if length(p)~=k || min(size(p))~=1 || any(p<1) || any(floor(p)~=p) + error('P must contain K positive integer elements if a vector.'); + end +end +% o +if length(o)==1 + if o<0 || floor(o)~=o + error('O must be a non-neagative integer if scalar.'); + end + o = ones(k,1) * o; +else + if length(o)~=k || min(size(o))~=1 || any(o<0) || any(floor(o)~=o) + error('O must contain K non-negative integer elements if a vector.'); + end +end +% q +if length(q)==1 + if q<0 || floor(q)~=q + error('Q must be a non-neagative integer if scalar.'); + end + q = ones(k,1) * q; +else + if length(q)~=k || min(size(q))~=1 || any(q<0) || any(floor(q)~=q) + error('Q must contain K non-negative integer elements if a vector.'); + end +end +if any(o>0) && isempty(dataAsym) + error('DATAASYM must be non-empty if O>0.') +end + +if ~isempty(startingVals) + if size(startingVals,2)>size(startingVals,1) + startingVals = startingVals'; + end + if length(startingVals)<(k+sum(p)+sum(o)+sum(q)) + error('STARTINGVALS should be a K+sum(P)+sum(O)+sum(Q) by 1 vector'); + end +end + +%Make sure options is a valid option structure +if isempty(options) + options = optimset('fminunc'); + options.Display = 'off'; + options.LargeScale = 'off'; +end + +try + optimset(options); +catch ME + error('OPTIONS is not a valid options structure'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +if ndims(data)==3 + [k,nothing,t]=size(data); +else + [t,k] = size(data); + temp = zeros(k,k,t); + for i=1:t + temp(:,:,i) = data(i,:)'*data(i,:); + dataAsym(:,:,i) = (data(i,:).*(data(i,:)<0))'*(data(i,:).*(data(i,:)<0)); + end + data = temp; +end + +tarchParameters = cell(k,1); +ht=cell(k,1); +tarchVcv=cell(k,1); +tarchScores = cell(k,1); +htMat = zeros(t,k); +volData = zeros(t,k); + +for i=1:k + % Prepare the data + tempData = sqrt(data(i,i,:)); + if o(i)>0 + tempData = tempData .* ((dataAsym(i,i,:)<=0) -(dataAsym(i,i,:)>0)); + end + volData(:,i) = squeeze(tempData); + tarchStartingVals = []; + if ~isempty(startingVals) + parameterEnd = i + sum(p(1:i)) + sum(o(1:i)) + sum(q(1:i)); + parameterStart = parameterEnd - 1 - p(i) - o(i) - q(i) + 1; + tarchStartingVals = startingVals(parameterStart:parameterEnd); + end + [tarchParameters{i},nothing,ht{i},nothing,tarchVcv{i},tarchScores{i}]=tarch(volData(:,i),p(i),o(i),q(i),[],2,tarchStartingVals,options); + htMat(:,i) = ht{i}; +end + +htArray = zeros(k,k,t); +for i=1:k + for j=i:k + htArray(i,j,:) = reshape(sqrt(htMat(:,i).*htMat(:,j)),[1 1 t]); + htArray(j,i,:) = htArray(i,j,:); + end +end + +stdData = data./htArray; +R = mean(stdData,3); +R = R./sqrt(diag(R)*diag(R)'); +parameters = zeros(sum(p)+sum(o)+sum(q)+k*(k-1)/2,1); +parameterCount = 1; + + +for i=1:k + parameterCountEnd = parameterCount + sum(1+p(i)+o(i)+q(i)); + parameters(parameterCount:parameterCountEnd-1) = tarchParameters{i}; + parameterCount = parameterCountEnd; +end +corrIndex = parameterCount:parameterCount+(k*(k-1)/2) - 1; +parameters(corrIndex) = corr_vech(R); + +% Compute the LL and covariance +if nargout>1 + [ll, lls, ht] = ccc_mvgarch_joint_likelihood(parameters,data,volData,p,o,q); + ll = - ll; +end +% Inference +if nargout>3 + A = zeros(length(parameters)); + parameterCount = 1; + scores = zeros(t,length(parameters)); + for i=1:k + parameterCountEnd = parameterCount + sum(1+p(i)+o(i)+q(i)) - 1; + index = parameterCount:parameterCountEnd; + A(index,index) = tarchVcv{i}^(-1); + scores(:,index) = tarchScores{i}; + parameterCount = parameterCountEnd + 1; + end + corrParameters = parameters(corrIndex); + A(corrIndex,:) = hessian_2sided_nrows(@ccc_mvgarch_joint_likelihood,parameters,k*(k-1)/2,data,volData,p,o,q); + [nothing,scores(:,corrIndex)] = gradient_2sided(@ccc_mvgarch_likelihood,corrParameters,data,htMat); + A = A/t; + B = covnw(scores,0,0); + Ainv = A^(-1); + VCV = Ainv*B*Ainv'/t; +end \ No newline at end of file diff --git a/multivariate/ccc_mvgarch_joint_likelihood.m b/multivariate/ccc_mvgarch_joint_likelihood.m new file mode 100644 index 0000000..e95c5e2 --- /dev/null +++ b/multivariate/ccc_mvgarch_joint_likelihood.m @@ -0,0 +1,76 @@ +function [ll, lls, ht] = ccc_mvgarch_joint_likelihood(parameters,data,volData,p,o,q) +% Log likelihood for CCC_MVGARCH inference. This function is only used for computing the Hessian. +% +% USAGE: +% [LL, LLS] = ccc_mvgarch_joint_likelihood(PARAMETERS,DATA,VOLDATA,P,O,Q) +% +% INPUTS: +% PARAMETERS - a parameter vector of the form +% [tarch(1)' tarch(2)' ... tarch(k)' corr_vech(R)] +% where each set of TARCH parameters is +% tarch(i) = +% [omega(i) alpha(i,1) ... alpha(i,p(i)) gamma(i,1) +% ... gamma(i,o(i)) beta(i,1) ... beta(i,q(i))]' +% and where R is the constant conditional correlation. +% DATA - K by K by T 3D array of positive semi-definite matrices. +% VOLDATA - T by K matrix of data used in estimating the volatility models. +% P - K by 1 vector of symmetric innovation orders for the TARCH models +% O - K by 1 vector of asymmetric innovation orders for the TARCH models +% Q - K by 1 vector of lagged variance innovation orders for the TARCH models +% +% OUTPUTS: +% LL - Minus 1 times the log likelihood +% LLS - Time series of log likelihoods (Also multiplied by -1) +% +% COMMENTS: +% See also CCC_MVGARCH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 4 Date: 10/28/2009 + +[k,nothing,t]=size(data); +htMat = zeros(t,k); +% Construct the variances +backCastlength = max(floor(t^(1/2)),1); +backCastWeights = .05*(.9.^(0:backCastlength )); +backCastWeights = backCastWeights/sum(backCastWeights); + +parameterCount = 1; +for i=1:k + epsilon = volData(:,i); + m = max([p(i) o(i) q(i)]); + fdata = [mean(epsilon.^2)*ones(m,1) ; epsilon.^2]; + %fIepsilon is fepsilon*(epsilon<0) + fIdata = [0.5*mean(epsilon.^2)*ones(m,1) ; epsilon.^2.*(epsilon<0)]; + backCast = backCastWeights*(volData(1:backCastlength+1,i).^2); + if backCast==0 + backCast=mean(epsilon.^2); + end + + T = length(fdata); + parameterCountEnd = parameterCount + (1+p(i)+o(i)+q(i)) - 1; + tarchParameters = parameters(parameterCount:parameterCountEnd); + variance=tarch_core(fdata,fIdata,tarchParameters,backCast,p(i),o(i),q(i),m,T,2); + htMat(:,i) = variance(m+1:T); + parameterCount = parameterCountEnd+1; +end +% Construct the correlation matrix +R = corr_ivech(parameters(parameterCount:parameterCount+(k*(k-1)/2)-1)); +% Compute the likelihood +Rinv = inv(R); +LogDetR = log(det(R)); +llconst = k*log(2*pi); +lls = zeros(t,1); +for i=1:t + stdResid = data(:,:,i)./sqrt(htMat(i,:)'*htMat(i,:)); + lls(i) = 0.5 * (llconst + sum(log(htMat(i,:))) + LogDetR + trace(Rinv*stdResid)); +end +ll = sum(lls); +if nargout>2 + ht = zeros(k,k,t); + for i=1:t + h12 = sqrt(htMat(i,:)); + ht(:,:,i) = R .* (h12'*h12); + end +end diff --git a/multivariate/ccc_mvgarch_likelihood.m b/multivariate/ccc_mvgarch_likelihood.m new file mode 100644 index 0000000..c6fb5dd --- /dev/null +++ b/multivariate/ccc_mvgarch_likelihood.m @@ -0,0 +1,36 @@ +function [ll, lls] = ccc_mvgarch_likelihood(parameters,data,htMat) +% Log likelihood for CCC_MVGARCH inference. This function is only used for computing scores. +% +% USAGE: +% [LL, LLS] = ccc_mvgarch_likelihood(PARAMETERS,DATA,HTMAT) +% +% INPUTS: +% PARAMETERS - A vector of constant correlation parameters, K*(K-1)/2 by 1 where +% R = corr_ivech(PARAMETERS) +% DATA - K x K x T 3D array of positive semi-definite matrices. +% HTMAT - T by K matrix of fit conditional variances. +% +% OUTPUTS: +% LL - Minus 1 times the log likelihood +% LLS - Time series of log likelihoods (Also multiplied by -1) +% +% COMMENTS: +% See also CCC_MVGARCH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 4 Date: 10/28/2009 + +[k, nothing, t] = size(data); +% Construct the correlation matrix +R = corr_ivech(parameters); +% Compute the likelihood +Rinv = inv(R); +LogDetR = log(det(R)); +llconst = k*log(2*pi); +lls = zeros(t,1); +for i=1:t + stdResid = data(:,:,i)./sqrt(htMat(i,:)'*htMat(i,:)); + lls(i) = 0.5 * (llconst + sum(log(htMat(i,:))) + LogDetR + trace(Rinv*stdResid)); +end +ll = sum(lls); diff --git a/multivariate/ccc_mvgarch_simulate.m b/multivariate/ccc_mvgarch_simulate.m new file mode 100644 index 0000000..8c1162e --- /dev/null +++ b/multivariate/ccc_mvgarch_simulate.m @@ -0,0 +1,167 @@ +function [simulatedata,ht,pseudorc]=ccc_mvgarch_simulate(t,k,parameters,p,o,q,m) +% TARCH(p,o,q) - Constant Conditional Correlation MV GARCH simulation +% +% USAGE: +% [SIMULATEDATA, HT, PSEUDORC] = ccc_mvgarch_simulate(T, K, PARAMETERS, P, O, Q, M) +% +% INPUTS: +% T - Length of the time series to be simulated +% K - Cross-sectional dimension +% PARAMETERS - a parameter vector of the form +% [tarch(1)' tarch(2)' ... tarch(k)' corr_vech(R)] +% where each set of TARCH parameters is +% tarch(i) = +% [omega(i) alpha(i,1) ... alpha(i,p(i)) gamma(i,1) +% ... gamma(i,o(i)) beta(i,1) ... beta(i,q(i))]' +% and where R is the constant conditional correlation. +% P - Positive, scalar integer representing the number of symmetric innovations -OR- +% K by 1 vector of individual symmetric innovations order +% O - Non-negative, scalar integer representing the number of asymmetric lags -OR- +% K by 1 vector of individual asymmetric innovations order +% Q - Non-negative, scalar integer representing the number of conditional variance lags -OR- +% K by 1 vector of individual conditional variance lags +% M - [OPTIONAL] Number of ``intradaily'' returns to simulate to pseudo-Realized +% Covariance. If omitted, set to 72. +% +% OUTPUTS: +% SIMULATEDATA - A time series with constant conditional correlation covariance +% HT - A [k k t] matrix of simulated conditional covariances +% PSEUDORC - A [k k t] matrix of pseudo-Realized Covariances +% +% COMMENTS: +% The conditional variance, H(t), of a constant conditional correlation model is +% H(t) = Sigma(t) * R * Sigma(t) +% +% where Sigma(t) is a diagonal matrix with TARCH(P,O,Q) volatilities on its diagonal. +% +% Pseudo Realized Covariances are simulated by generating m-intra daily returns from a N(0,1/m) +% and computing the Realized Covariance of these. These were used in Patton and Sheppard (2009) +% when evaluating variance and covariance specifications in a Monte Carlo. If M=1, then PSEUDORC +% is just the outer product of the SIMULATEDATA. +% +% NOTE: This program generates 2000 more than required to minimize any start-up bias +% +% See also TARCH_SIMULATE, SCALAR_VT_VECH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 4 Date: 10/28/2009 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 6 + m=[]; + case 7 + % nothing + otherwise + error('MFEToolbox:Input','6 or 7 inputs required.'); +end + +% t +if ~isscalar(t) || t<0 || floor(t)~=t + error('T must be a positive integer.'); +end +% k +if ~isscalar(k) || k<2 || floor(k)~=k + error('K must be a positive integer greater than or equal to 2.'); +end +% p +if length(p)==1 + if p<1 || floor(p)~=p + error('P must be a positive integer if scalar.'); + end + p = ones(k,1) * p; +else + if length(p)~=k || min(size(p))~=1 || any(p<1) || any(floor(p)~=p) + error('P must contain K positive integer elements if a vector.'); + end +end +% o +if length(o)==1 + if o<0 || floor(o)~=o + error('O must be a non-neagative integer if scalar.'); + end + o = ones(k,1) * o; +else + if length(o)~=k || min(size(o))~=1 || any(o<0) || any(floor(o)~=o) + error('O must contain K non-negative integer elements if a vector.'); + end +end +% q +if length(q)==1 + if q<0 || floor(q)~=q + error('Q must be a non-neagative integer if scalar.'); + end + q = ones(k,1) * q; +else + if length(q)~=k || min(size(q))~=1 || any(q<0) || any(floor(q)~=q) + error('Q must contain K non-negative integer elements if a vector.'); + end +end +% m +if isempty(m) + m = 72; +end +if ~isscalar(m) || floor(m)~=m || m<1 + error('M must be a positive integer.') +end +% parameters +parameterCount = k + sum(p) + sum(o) + sum(q) + k*(k-1)/2; +if size(parameters,2)>size(parameters,1) + parameters = parameters'; +end +n = length(parameters); +if n~=parameterCount + error('PARAMETERS must have K + sum(P) + sum(O) + sum(Q) + K*(K-1)/2 elements.'); +end +R = corr_ivech(parameters(n-k*(k-1)/2+1:n)); +if min(eig(R))<=0 || any(any(R~=R')) + error('The correlation matrix R must be postive definite.'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +% Get the correlation matrix + + +%Set the burnin amount, 2000 is probably reasonable +burnin=2000; +%Up t by the burnin amount +t=t+burnin; + + + +%Draw some normal random numbers +intraRandomNums=randn(m*t,k)*sqrt(1/m); +intraRandomNums = intraRandomNums * R^(0.5); +randomNums = cumsum(intraRandomNums); +randomNums = diff([zeros(1,k);randomNums(m:m:m*t,:)]); + +parameterStart = 1; +data = zeros(t,k); +htMat = zeros(t,k); +for i=1:k + parameterEnd = parameterStart + (1+p(i)+o(i)+q(i)) - 1; + tarchParameters = parameters(parameterStart:parameterEnd); + [data(:,i),htMat(:,i)]=tarch_simulate(randomNums(:,i),tarchParameters,p(i),o(i),q(i),'NORMAL',2); + parameterStart = parameterEnd + 1; +end + +%Initialize the covariance +ht=repmat(R,[1 1 t]); +pseudorc=zeros(k,k,t); +for i=1:t + vol = sqrt(htMat(i,:)); + ht(:,:,i) = ht(:,:,i) .* (vol'*vol); + r = intraRandomNums((i-1)*m+1:i*m,:).*repmat(vol,m,1); + pseudorc(:,:,i) = r'*r; +end + +%Truncate the data and the covariance +simulatedata=data(burnin+1:t,:); +pseudorc = pseudorc(:,:,burnin+1:t); +ht=ht(:,:,burnin+1:t); \ No newline at end of file diff --git a/multivariate/matrix_garch.m b/multivariate/matrix_garch.m new file mode 100644 index 0000000..5c3084f --- /dev/null +++ b/multivariate/matrix_garch.m @@ -0,0 +1,259 @@ +function [parameters, ll, ht, VCV, scores, diagnostics] = matrix_garch(data,dataAsym,p,o,q,startingvals,options) +% Estimation of symmetric and asymmetric MATRIX multivariate GARCH models +% +% USAGE: +% [PARAMETERS,LL,HT,VCV,SCORES,DIAGNOSTICS] = matrix_garch(DATA,DATAASYM,P,O,Q,STARTINGVALS,OPTIONS) +% +% INPUTS: +% DATA - A T by K matrix of zero mean residuals -OR- +% K by K by T array of covariance estimators (e.g. realized covariance) +% DATAASYM - [OPTIONAL] K by K by T array of asymmetric covariance +% estimators (e.g. RC scaled by indicator functions) +% P - Positive, scalar integer representing the number of lags of the innovation process +% O - Non-negative scalar integer representing the number of asymmetric lags to include +% Q - Non-negative scalar integer representing the number of lags of conditional covariance +% STARTINGVALS - [OPTIONAL] INCOMPLETE +% OPTIONS - [OPTIONAL] Options to use in the optimization (fminunc) +% +% OUTPUTS: +% PARAMETERS - K(K+1)/2*(1+P+O+Q) by 1 vector of parameters of the form +% [vech(C)' vech(A(1))' ... vech(A(P))' vech(G(1))' ... +% vech(G(O))' vech(B(1))' ... vech(B(Q))']' +% LL - The log likelihood at the optimum +% HT - A [K K T] dimension matrix of conditional covariances +% VCV - A numParams^2 square matrix of robust parameter covariances (A^(-1)*B*A^(-1)*t^(-1)) +% SCORES - A T by numParams matrix of individual scores +% DIAGNOSTICS - Structure containing some diagnostic information +% +% COMMENTS: +% The conditional variance, H(t), of a MATRIX GARCH is modeled as follows: +% +% H(t) = CC' + A(1)A(1)'.*r_{t-1}'*r_{t-1} + ... + A(P)A(P)'.*r_{t-P}'*r_{t-P} +% + G(1)G(1)'.*n_{t-1}'*n_{t-1} + ... + G(O)G(O)'.*n_{t-P}'*n_{t-P} +% + B(1)B(1)'.*H(t-1) +...+ B(Q)B(Q)'.*H(t-q) +% +% where n_{t} = r_{t} .* (r_{t}<0). If using realized measures, the +% RM_{t-1} replaces r_{t-1}'*r_{t-1}, and the asymmetric version +% replaces n_{t-1}'*n_{t-1} +% +% EXAMPLES: +% % Estimation of a symmetric MATRIX GARCH(1,0,1) model +% parameters = matrix_garch(data,[],1,0,1); +% % Estimation of an asymmetric MATRIX GARCH(1,0,1) model +% parameters = matrix_garch(data,[],1,1,1); +% % Estimation of a symmetric MATRIX GARCH(1,0,1) model using realized covariacne +% data = RC % K by K by T 3D of realized covariacne +% parameters = matrix_garch(RC,[],1,0,1); + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 10/28/2009 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 3 + o=0; + q=0; + startingvals=[]; + options = []; + case 4 + q=0; + startingvals=[]; + options = []; + case 5 + startingvals=[]; + options = []; + case 6 + options = []; + case 7 + otherwise + error('Between 2 and 6 arguments required.') +end + +%data should be TxK, T>K +if ndims(data)==2 + [t,k]=size(data); + if ~isempty(dataAsym) + error('If DATA is a T by K matrix, DATAASYM must be empty.'); + end + temp = zeros(k,k,t); + dataAsym = zeros(k,k,t); + for i=1:t + temp(:,:,i) = data(i,:)'*data(i,:); + dataAsym(:,:,i) = (data(i,:).*(data(i,:)<0))'*(data(i,:).*(data(i,:)<0)); + end + data = temp; +elseif ndims(data)==3 + [k,m,t] = size(data); + if m~=k + error('DATA must be K by K by T is a 3D array.'); + end + if ~isempty(dataAsym) + if ndims(dataAsym)~=3 + error('DATAASYM must be a 3D array with the same dimensions as DATA'); + end + [k2,m2,t2]=size(dataAsym); + if any([k m t]~=[k2 m2 t2]) + error('DATAASYM must be a 3D array with the same dimensions as DATA'); + end + end +end +k2 = k*(k+1)/2; +if min(t,k)<2 || tK>1'); +end + +%p, o, q much be non-negative scalars +if length(p)>1 || any(p<1) || floor(p)~=p + error('P must be a positive scalar'); +end +if isempty(o) + o = 0; +end +if length(o)>1 || any(o<0) || floor(o)~=o + error('O must be a non-negative scalar'); +end +if o>0 && isempty(dataAsym) + error('DATAASYM must be non-empty if O>0.') +end + +if isempty(q) + q = 0; +end +if length(q)>1 || any(q<0) || floor(q)~=q + error('Q must be a non-negative scalar'); +end + +% Startingvals must have (k*(k+1)/2)(1+p+o+q) parameters +if ~isempty(startingvals) + if size(startingvals,2)>size(startingvals,1) + startingvals = startingvals'; + end + if length(startingvals)<(p+o+q) + error('STARTINGVALS should be a P+O+Q by 1 vector'); + end + % Only validate if provided + % FIXME: Fix Validation + % TODO: Fix Validation + A=startingvals(1:p); + G=startingvals(p+1:p+o); + B=startingvals(p+o+1:p+o+q); + if (sum(A)+sum(G)/kappa+sum(B))>=.999998 + error('Weighted sum of STATINGVALUES must be less than 1. See Comments.'); + end + if any(A<0) || any(B<0) || any(G<0) + error('STARTINGVALS must all be nonnegative.'); + end +end + +%Make sure options is a valid option structure +if isempty(options) + options=optimset('fminunc'); + options.Display='iter'; + options.Diagnostics='on'; + options.LargeScale='off'; + options.MaxFunEvals = 1000*k2*(1+p+o+q); +end +try + optimset(options); +catch ME + error('OPTIONS is not a valid options structure'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Compute the backCast +backCast = zeros(k); +backCastAsym = zeros(k); +tau = max(ceil(sqrt(t)),k); +weights = .06 * .94.^(0:tau); +weights = weights / sum(weights); +for i=1:tau + backCast = backCast + weights(i) * data(:,:,i); + if o>0 + backCastAsym = backCastAsym + weights(i) * dataAsym(:,:,i); + end +end + +%Get starting values from scalar_vt_vech +if isempty(startingvals) + startingOptions=optimset('fminunc'); + startingOptions.Display='off'; + startingOptions.Diagnostics='off'; + startingOptions.LargeScale='off'; + startingOptions.TolX = 1e-4; + startingOptions.TolFun = 1e-4; + [scalarVechStartingvals,n,n,n,n,diagnostics] = scalar_vt_vech(data,dataAsym,p,o,q,[],startingOptions); + CpC = diagnostics.intercept; + + startingvals = zeros(k2 * (1+p+o+q),1); + startingvals(1:k2) = chol2vec(chol(CpC)'); + index = k2; + for i=1:(p+o+q) + matrixParameters = scalarVechStartingvals(i)*(.02*eye(k) + .98*ones(k)); + startingvals(index+1:index+k2) = chol2vec(chol(matrixParameters)'); + index = index + k2; + end +end + + +warning('off','MATLAB:illConditionedMatrix') +ll0 = matrix_garch_likelihood(startingvals,data,dataAsym,p,o,q,backCast,backCastAsym); +[parameters,ll,exitflag,output]=fminunc('matrix_garch_likelihood',startingvals,options,data,dataAsym,p,o,q,backCast,backCastAsym); + +%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Estimation Robustification +%%%%%%%%%%%%%%%%%%%%%%%%%%% +if exitflag<=0 && ll1 + [ll,lls,ht]=matrix_garch_likelihood(parameters,data,dataAsym,p,o,q,backCast,backCastAsym); + ll=-ll; +end + +%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Compute the VCV +%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargout>3 + [VCV,A,B,scores]=robustvcv('matrix_garch_likelihood',parameters,0,data,dataAsym,p,o,q,backCast,backCastAsym); +end + +%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Compute the VCV +%%%%%%%%%%%%%%%%%%%%%%%%%%% +diagnostics = []; +diagnostics.EXITFLAG=exitflag; +diagnostics.ITERATIONS=output.iterations; +diagnostics.FUNCCOUNT=output.funcCount; +diagnostics.MESSAGE=output.message; +parameterMatrices = zeros(k,k,1+p+o+q); +index = 0; +for i=1:(1+p+o+1) + temp = vec2chol(parameters(index+1:index+k2)); + parameterMatrices(:,:,i) = temp*temp'; + index=index+k2; +end +diagnostics.C = parameterMatrices(:,:,1); +diagnostics.A = parameterMatrices(:,:,2:p+1); +if o>0 + diagnostics.G = parameterMatrices(:,:,p+2:p+o+1); +else + diagnostics.G = []; +end + +if q>0 + diagnostics.B = parameterMatrices(:,:,p+o+2:p+o+q+1); +else + diagnostics.B = []; +end diff --git a/multivariate/matrix_garch_display.m b/multivariate/matrix_garch_display.m new file mode 100644 index 0000000..9d57331 --- /dev/null +++ b/multivariate/matrix_garch_display.m @@ -0,0 +1,91 @@ +function [C,A,G,B] = matrix_garch_display(parameters,p,o,q) +% Displays the MATRIX garch estimates in a friendly format +% +% USAGE: +% [C,A,G,B] = matrix_garch(PARAMETERS,P,O,Q) +% +% INPUTS: +% PARAMETERS - Output from callig matrix_garch +% P - Positive, scalar integer representing the number of lags of the innovation process +% O - Non-negative scalar integer representing the number of asymmetric lags to include +% Q - Non-negative scalar integer representing the number of lags of conditional covariance +% +% OUTPUTS: +% C - K by K matrixd containing the constant +% A - A [K K P] dimension matrix containing the parameters of the symmetric terms +% G - A [K K O] dimension matrix containing the parameters of the asymmetric terms +% B - A [K K B] dimension matrix containing the parameters of the lagged conditional variance +% +% COMMENTS: +% +% EXAMPLES: +% Display the parameters of an asymmetric MATRIX GARCH(1,1,1) process +% [simulatedData, Ht, pseudoRC] = scalar_vt_vech_simulate(1000, [.02 .04 .95], .01*eye(2), 1, 1, 1, 72); +% parameters = matrix_garch(simulatedData,[],1,1,1) +% [C,A,G,B] = matrix_garch_display(parameters,1,1,1) + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 3/10/2011 + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if size(parameters,2)>size(parameters,1) + parameters = parameters'; +end +if any(floor([p o q])~=[p o q]) || any ([p o q]<0) + error('P, O, and Q must all be non-negative integers.') +end +% Dimension +paraLen=length(parameters); +k2 = paraLen/(1+p+o+q); +if ~(floor(k2)==k2) + error('PARAMETERS does not have the expected number of elements: K*(K+1)/2*(1+P+O+Q)') +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +k = floor(sqrt(2*k2)); + + +parameterMatrices= zeros(k,k,1+p+o+q); +index = 0; +for i=1:(1+p+o+1) + temp = vec2chol(parameters(index+1:index+k2)); + parameterMatrices(:,:,i) = temp*temp'; + index=index+k2; +end + +C = parameterMatrices(:,:,1); +A = parameterMatrices(:,:,2:p+1); +G = parameterMatrices(:,:,2+p:1+p+o); +B = parameterMatrices(:,:,2+p+o:1+p+o+q); + +k1 = ceil(k/2); +dispStr = [repmat(' ',k1-1,1); 'H(t) =';repmat(' ',k-k1,1)]; +dispStr = [dispStr repmat(' ',k,1) repmat('[',k,1) num2str(C) repmat(']',k,1)]; +plus = [repmat(' ',k,1) [repmat(' ',k1-1,1); '+';repmat(' ',k-k1,1)]]; +for i=1:p + dispStr = [dispStr plus repmat(' ',k,1) repmat('[',k,1) num2str(A(:,:,i)) repmat(']',k,1)]; %#ok<*AGROW> + dispStr = [dispStr [repmat(' ',k1-1,15); '.*r(t-' num2str(i) ')r(t-' num2str(i) ')''';repmat(' ',k-k1,15)]]; +end +for i=1:o + dispStr = [dispStr plus repmat(' ',k,1) repmat('[',k,1) num2str(G(:,:,i)) repmat(']',k,1)]; + dispStr = [dispStr [repmat(' ',k1-1,15); '.*n(t-' num2str(i) ')n(t-' num2str(i) ')''';repmat(' ',k-k1,15)]]; +end +for i=1:q + dispStr = [dispStr plus repmat(' ',k,1) repmat('[',k,1) num2str(B(:,:,i)) repmat(']',k,1)]; + dispStr = [dispStr [repmat(' ',k1-1,8); '.*H(t-' num2str(i) ')';repmat(' ',k-k1,8)]]; +end + +disp(dispStr) +if o>0 + disp('Note: r(t-i)r(t-i)'' is the RC, and n(t-i)n(t-i)'' is the asymmetric RC term, if the model used realized measures.') +else + disp('Note: r(t-i)r(t-i)'' is the RC if the model used realized measures.') +end + diff --git a/multivariate/matrix_garch_likelihood.m b/multivariate/matrix_garch_likelihood.m new file mode 100644 index 0000000..cf346be --- /dev/null +++ b/multivariate/matrix_garch_likelihood.m @@ -0,0 +1,87 @@ +function [ll,lls,Ht]=matrix_garch_likelihood(parameters,data,dataAsym,p,o,q,backCast,backCastAsym) +% Log likelihood for MATRIX_GARCH(P,O,Q) estimation +% +% USAGE: +% [LL, LLS, HT] = matrix_garch_likelihood(PARAMETERS,DATA,DATAASYM,P,O,Q,BACKCAST,BACKCASTASYM) +% +% INPUTS: +% PARAMETERS - A vector of vech GARCH process parameters: [alpha beta]' or +% [vech(C)' alpha beta]' if ISJOINT +% DATA - K by K by T matrix of covariance innovations +% DATAASYM - K by K by T matrix of asymmetric covariance innovations +% P - Positive, scalar integer representing the number of lags of the innovation process +% O - Non-negative scalar integer representing the number of lags of asymmetric process +% Q - Non-negative scalar integer representing the number of lags of conditional covariance +% BACKCAST - Back cast value for starting the recursion +% BACKCASTASYM - Back cast value (asymetric terms) for starting the recursion +% +% OUTPUTS: +% LL - Minus 1 times the log likelihood +% LLS - Time series of log likelihoods (Also multiplied by -1) +% HT - Time series of conditional covariances +% +% COMMENTS: +% See also MATRIX_GARCH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 4 Date: 10/28/2009 + +[k,nothing,T]=size(data); +k2 = k*(k+1)/2; +%If nargin~=7, then we don't need to transform the parameters +parameterMatrices= zeros(k,k,1+p+o+q); +index = 0; +for i=1:(1+p+o+q) + temp = vec2chol(parameters(index+1:index+k2)); + parameterMatrices(:,:,i) = (temp*temp'+temp*temp')/2; + index=index+k2; +end +%Initialize the covariance +Ht=repmat(backCast,[1 1 T]); + +%Initialize the log likelihood +lls=zeros(T,1); + +%Compute the likelihood constant. +likconst=k*log(2*pi); + +%Perform the recursion +for t=1:T; + Ht(:,:,t)=parameterMatrices(:,:,1); + for j=1:p + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,j+1).*backCast; + else + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,j+1).*data(:,:,t-j); + end + end + for j=1:o + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,p+j+1).*backCastAsym; + else + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,p+j+1).*dataAsym(:,:,t-j); + end + end + for j=1:q + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,p+o+j+1).*backCast; + else + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,p+o+j+1).*Ht(:,:,t-j); + end + end + % Replace these lines to make it work better with poorle conditioned data + % likelihoods(i)=likconst+(log(det(Ht(:,:,t)))+data(i,:)*Ht(:,:,t)^(-1)*data(i,:)'); + + %This is a trick to ensure better numerical stability + Q=sqrt(diag(Ht(:,:,t))); + R=Ht(:,:,t)./(Q*Q'); + stdresid=data(:,:,t)./(Q*Q'); + lls(t)=0.5*(likconst+2*sum(log(Q))+log(det(R))+trace(R^(-1)*stdresid)); +end +ll = sum(lls); + +% This is a hack since the estimation is unconstrained +if isnan(ll) || isinf(ll) || ll>1e7 + ll = 1e7; +end \ No newline at end of file diff --git a/multivariate/matrix_garch_simulate.m b/multivariate/matrix_garch_simulate.m new file mode 100644 index 0000000..50f224f --- /dev/null +++ b/multivariate/matrix_garch_simulate.m @@ -0,0 +1,198 @@ +function [simulatedata,ht,pseudorc]=matrix_garch_simulate(t,k,parameters,p,o,q,m) +% Simulation of symmetric and asymmetric MATRIX multivariate GARCH models +% +% USAGE: +% [SIMULATEDATA, HT, PSEUDORC] = matrix_garch_simulate(T, K, PARAMETERS, P, O, Q, M) +% +% INPUTS: +% T - Length of the time series to be simulated +% K - Cross-sectional dimension +% PARAMETERS - A 3-D matrix of K by K matrices where +% CC' = PARAMETERS(:,:,1), AA'(j)=PARAMETERS(:,:,1+j), +% GG'(j) = PARAMETERS(:,:,1+P+j), BB'(j)=PARAMETERS(:,:,1+P+Q+j) +% -OR- a K(K+1)/2*(1+P+O+Q) by 1 vector of parameters of +% the form returned my calling matrix_garch +% P - Positive, scalar integer representing the number of lags of the innovation process +% O - Non-negative scalar integer representing the number of asymmetric lags to include +% Q - Non-negative scalar integer representing the number of lags of conditional covariance +% M - [OPTIONAL] Number of ``intradaily'' returns to simulate to pseudo-Realized +% Covariance. If omitted, set to 72. +% +% OUTPUTS: +% SIMULATEDATA - A time series with constant conditional correlation covariance +% HT - A [k k t] matrix of simulated conditional covariances +% PSEUDORC - A [k k t] matrix of pseudo-Realized Covariances +% +% COMMENTS: +% The conditional variance, H(t), of a MATRIX GARCH is modeled as follows: +% +% H(t) = CC' + AA'(1).*r_{t-1}'*r_{t-1} + ... + AA'(P).*r_{t-P}'*r_{t-P} +% + GG(1)'.*n_{t-1}'*n_{t-1} + ... + GG(O)'.*n_{t-P}'*n_{t-P} +% + BB(1)'.*H(t-1) +...+ BB(Q)'.*H(t-q) +% +% where n_{t} = r_{t} .* (r_{t}<0). If using realized measures, the +% RM_{t-1} replaces r_{t-1}'*r_{t-1}, and the asymmetric version +% replaces n_{t-1}'*n_{t-1} +% +% Pseudo Realized Covariances are simulated by generating m-intra daily returns from a N(0,1/m) +% and computing the Realized Covariance of these. These were used in Patton and Sheppard (2009) +% when evaluating variance and covariance specifications in a Monte Carlo. If M=1, then PSEUDORC +% is just the outer product of the SIMULATEDATA. +% +% NOTE: This program generates 2000 more than required to minimize any start-up bias +% +% See also TARCH_SIMULATE, CCC_GARCH_SIMULATE, MATRIX_GARCH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 3/10/2011 + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 6 + m=[]; + case 7 + % nothing + otherwise + error('MFEToolbox:Input','6 or 7 inputs required.'); +end + +% t +if ~isscalar(t) || t<0 || floor(t)~=t + error('T must be a positive integer.'); +end +% k +if ~isscalar(k) || k<2 || floor(k)~=k + error('K must be a positive integer greater than or equal to 2.'); +end +% p +if ~isscalar(p) || p<1 || floor(p)~=p + error('P must be a positive integer if scalar.'); +end + +% o + +if ~isscalar(o) || o<0 || floor(o)~=o + error('O must be a non-neagative integer if scalar.'); +end +% q + +if ~isscalar(q) || q<0 || floor(q)~=q + error('Q must be a non-neagative integer if scalar.'); +end +% m +if isempty(m) + m = 72; +end +if ~isscalar(m) || floor(m)~=m || m<1 + error('M must be a positive integer.') +end +% parameters +k2 = k*(k+1)/2; +if ndims(parameters)==2 + parameterCount = k*(k+1)/2 *(1+ p + o + q); + if size(parameters,2)>size(parameters,1) + parameters = parameters'; + end + if length(parameters)~=parameterCount + error('PARAMETERS must be K(K+1)/28(1+P+O+Q) when using a vector.') + end + parameterMatrices= zeros(k,k,1+p+o+q); + index = 0; + for i=1:(1+p+o+1) + temp = vec2chol(parameters(index+1:index+k2)); + parameterMatrices(:,:,i) = (temp*temp'+temp*temp')/2; + index=index+k2; + end + parameters = parameterMatrices; +elseif ndims(parameters)==3 + if any(size(parameters)~=[k k 1+p+o+q]) + error('PARAMETERS must be K by K by (1+P+O+Q) when using a 3-D matrix.') + end +else + error('The size of PARAMETERS is not compatible with this function.') +end + +% Check stationarity +sumParameters = zeros(k); +for i=2:size(parameterMatrices,3) + if i<=(p+1) || i>(1+p+o) + w=1; + else + w=0.5; + end + sumParameters = sumParameters + w*parameterMatrices(:,:,i); +end +sumParameters = (sumParameters+sumParameters')/2; +if max(diag(sumParameters))>1 + warning('MFE::Nonstationary','The parameters do not correspond to a stationary solution. Check for overflow.') + uncond = parameters(:,:,1)/.005; +else + uncond = parameters(:,:,1)./(ones(k)-sumParameters); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Set the burnin amount, 2000 is probably reasonable +burnin=2000; +%Up t by the burnin amount +t=t+burnin; + +%Draw some normal random numbers +intraRandomNums=randn(m*t,k)*sqrt(1/m); +randomNums = cumsum(intraRandomNums); +randomNums = diff([zeros(1,k);randomNums(m:m:m*t,:)]); + + +%Perform the recursion +backCast = uncond; +backCastAsym = uncond; +T = t; +Ht = zeros(k,k,T); +simulatedData = zeros(T,k); +for t=1:T; + Ht(:,:,t)=parameterMatrices(:,:,1); + for j=1:p + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,j+1).*backCast; + else + r = simulatedData(t-j,:); + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,j+1).*(r'*r); + end + end + for j=1:o + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,p+j+1).*backCastAsym; + else + n = simulatedData(t-j,:).*(simulatedData(t-j,:)<0); + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,p+j+1).*(n'*n); + end + end + for j=1:q + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,p+o+j+1).*backCast; + else + Ht(:,:,t)=Ht(:,:,t)+parameterMatrices(:,:,p+o+j+1).*Ht(:,:,t-j); + end + end + simulatedData(t,:) = randomNums(t,:)*Ht(:,:,t)^(0.5); +end + + + + + +%Initialize the covariance +pseudorc=zeros(k,k,t); +for t=1:T + r = intraRandomNums((t-1)*m+1:t*m,:)*Ht(:,:,t)^(0.5); + pseudorc(:,:,t) = r'*r; +end + +%Truncate the data and the covariance +simulatedata=simulatedData(burnin+1:t,:); +pseudorc = pseudorc(:,:,burnin+1:t); +ht=Ht(:,:,burnin+1:t); \ No newline at end of file diff --git a/multivariate/o_mvgarch.m b/multivariate/o_mvgarch.m new file mode 100644 index 0000000..56f2752 --- /dev/null +++ b/multivariate/o_mvgarch.m @@ -0,0 +1,180 @@ +function [parameters,ht,w,pc]=o_mvgarch(data,numfactors,p,o,q,startingVals,options) +% Estimates a multivariate GARCH model using Orthogonal or Factor Garch. Involves Principal Component +% Analysis to reduce volatility modelling to univariate garches. See Carrol 2000 (An Inrtoduction to O-Garch) +% +% USAGE: +% [PARAMETERS,HT,STDRESID,STDERRORS,A,B,WEIGHTS,PRINCIPALCOMPONETS,CUMR2]=o_mvgarch(DATA,NUMFACTORS,P,O,Q); +% +% INPUTS: +% DATA - A T by K matrix of zero mean residuals +% NUMFACTORS - The number of principal components to include in the MV_GARCH model +% P - Positive, scalar integer representing the number of symmetric innovations -OR- +% K by 1 vector of individual symmetric innovations order +% O - Non-negative, scalar integer representing the number of asymmetric lags -OR- +% K by 1 vector of individual asymmetric innovations order +% Q - Non-negative, scalar integer representing the number of conditional variance lags -OR- +% K by 1 vector of individual conditional variance lags +% +% OPTIONS - [OPTIONAL] A fminunc options structure to use in estimating the factor conditional +% variances +% +% OUTPUTS: +% PARAMETERS - a parameter vector of the form +% [tarch(1)' tarch(2)' ... tarch(NUMFACTORS)' diag(OMEGA)] +% where each set of TARCH parameters is +% tarch(i) = +% [omega(i) alpha(i,1) ... alpha(i,p(i)) gamma(i,1) +% ... gamma(i,o(i)) beta(i,1) ... beta(i,q(i))]' +% and where OMEGA is the diagonal matrix of idiosyncratic variances. +% If NUMFACTORS = k diag(OMEGA) is omitted since all values are 0. +% HT - A [K K T] dimension matrix of conditional covariances +% W - a K by K matrix of componet weights +% PC - a T by K matrix of principal componets +% +% COMMENTS: +% Models the conditional covariance of assets using the NUMFACTORS principal components with the +% highest contribution to total variation in the data. The conditional covariance is +% +% H_t = W*F_t*W' + Omega +% +% where F_t is a diagonal matrix of the conditional factor variances, W is a K by NUMFACTORS +% matrix of factor loadings and Omega is a diagonal matrix of (time-invariant) idiosyncratic +% variances. If NUMFACTORS = K when Omega = 0. +% +% See also PCA, CCC_MVGARCH, DCC_MVGARCH + + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 10/28/2009 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 5 + options = []; + startingVals = []; + case 6 + options = []; + case 7 + % Nothing + otherwise + error('5 to 7 arguments required.') +end + +[t,k] = size(data); + +if min(t,k)<2 || tK>1'); +end + +%p, o, q much be non-negative scalars + +% p +if length(p)==1 + if p<1 || floor(p)~=p + error('P must be a positive integer if scalar.'); + end + p = ones(numfactors,1) * p; +else + if length(p)~=numfactors || min(size(p))~=1 || any(p<1) || any(floor(p)~=p) + error('P must contain K positive integer elements if a vector.'); + end +end + +% o +if length(o)==1 + if o<0 || floor(o)~=o + error('O must be a non-neagative integer if scalar.'); + end + o = ones(numfactors,1) * o; +else + if length(o)~=numfactors || min(size(o))~=1 || any(o<0) || any(floor(o)~=o) + error('O must contain K non-negative integer elements if a vector.'); + end +end + +% q +if length(q)==1 + if q<0 || floor(q)~=q + error('Q must be a non-neagative integer if scalar.'); + end + q = ones(numfactors,1) * q; +else + if length(q)~=numfactors || min(size(q))~=1 || any(q<0) || any(floor(q)~=q) + error('Q must contain K non-negative integer elements if a vector.'); + end +end +if any(o>0) && isempty(dataAsym) + error('DATAASYM must be non-empty if O>0.') +end + +if ~isempty(startingVals) + if size(startingVals,2)>size(startingVals,1) + startingVals = startingVals'; + end + if length(startingVals)<(k+sum(p)+sum(o)+sum(q)) + error('STARTINGVALS should be a K+sum(P)+sum(O)+sum(Q) by 1 vector'); + end +end + +%Make sure options is a valid option structure +if isempty(options) + options = optimset('fminunc'); + options.Display = 'off'; + options.LargeScale = 'off'; +end + +try + optimset(options); +catch ME + error('OPTIONS is not a valid options structure'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +[w, pc]=pca(data,'outer'); + + + +weights = w(1:numfactors,:); +pcs = pc(:,1:numfactors); + +htMat = zeros(t,numfactors); +tarchParameters = cell(numfactors,1); +tarchHt = cell(numfactors,1); +tarchVcv = cell(numfactors,1); +tarchScores = cell(numfactors,1); +for i=1:numfactors + % Prepare the data + tarchStartingVals = []; + if ~isempty(startingVals) + parameterEnd = i + sum(p(1:i)) + sum(o(1:i)) + sum(q(1:i)); + parameterStart = parameterEnd - 1 - p(i) - o(i) - q(i) + 1; + tarchStartingVals = startingVals(parameterStart:parameterEnd); + end + [tarchParameters{i},nothing,tarchHt{i},nothing,tarchVcv{i},tarchScores{i}]=tarch(pcs(:,i),p(i),o(i),q(i),[],2,tarchStartingVals,options); + htMat(:,i) = tarchHt{i}; +end + + +if numfactors=1 + error('LAMBDA must be between 0 and 1.') +end + +if isempty(backCast) + endPoint = max(min(floor(log(.01)/log(lambda)),T),k); + weights = (1-lambda).*lambda.^(0:endPoint-1); + weights = weights/sum(weights); + backCast = zeros(k); + for i=1:endPoint + backCast = backCast + weights(i)*data(:,:,i); + end + +end + +backCast = (backCast+backCast)/2; +if min(eig(backCast))<0 + error('BACKCAST must be positive semidefinite if provided.') +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +Ht = zeros(k,k,T); +Ht(:,:,1) = backCast; +for i=2:T + Ht(:,:,i) = (1-lambda)*data(:,:,i-1) + lambda * Ht(:,:,i-1); +end \ No newline at end of file diff --git a/multivariate/riskmetrics2006.m b/multivariate/riskmetrics2006.m new file mode 100644 index 0000000..c3f0e71 --- /dev/null +++ b/multivariate/riskmetrics2006.m @@ -0,0 +1,171 @@ +function [Ht,weights] = riskmetrics2006(data,tau0,tau1,kmax,rho) +% Computes the Riskmetrics 2006 covariance, which is a weighted average of +% EWMA covariances +% +% USAGE: +% [HT,WEIGHTS] = riskmetrics2006(DATA,TAU0,TAU1,KMAX,RHO) +% +% INPUTS: +% DATA - A T by K matrix of zero mean residuals -OR- +% K by K by T array of covariance estimators (e.g. realized covariance) +% TAU0 - [OPTIONAL] Half-life of slowest EWMA +% TAU1 - [OPTIONAL] Half-life of fastest EWMA +% KMAX - [OPTIONAL] Number of EWMA components to use +% RHO - [OPTIONAL] Decay factor to use in half-lives. The +% half-lives used are TAU1, TAU1*RHO, TAU1*RHO^2, ... +% +% OUTPUTS: +% HT - A [K K T] dimension matrix of conditional covariances +% WEIGHTS - A T by T matrix which contains the final weights used +% computing all conditional covariances. WEIGHT(i,j) +% contains the weight of the outer-product in time period j +% in the covariance forecast at period i+1 +% +% COMMENTS: +% The conditional variance, H(t), of a RM2006 covariance model +% +% H(t) = w(i)*Htilde(t,i) +% +% where Htilde(t,i) is an EWMA covariance, i=1,2,..., and +% +% w(i) = 1-log(TAU1^((i-1)*RHO))/log(TAU0) +% +% where the weights have been normalized so that they sum to 1. All +% EWMAs are initialized using a backward EWMA with the same decay. +% +% EXAMPLES: +% RiskMetrics 2006 methodology using the suggested reference values +% tau0 = 1560; +% tau1 = 4; +% taumax = 512; +% rho = sqrt(2); +% kmax = round(log(taumax/tau1)/log(rho)); % 14 +% Ht = riskmetrics2006(data,tau0,tau1,kmax,rho) +% +% RiskMetrics 1994 methodology using .94 as a special case of RM2006 +% tau0 = 1560; % Does not matter +% rho = 1; % Does not matter +% tau1 = -1/log(.94); +% kmax = 1; +% Ht = riskmetrics2006(data,tau0,tau1,kmax,rho) + + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 03/10/2011 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 1 + tau0=[]; + tau1=[]; + kmax=[]; + rho =[]; + case 2 + tau1=[]; + kmax=[]; + rho =[]; + case 3 + kmax=[]; + rho =[]; + case 4 + rho =[]; + case 5 + % Nothing + otherwise + error('1 to 5 inputs required.') +end + +if isempty(tau0) + tau0 = 1560; +end +if isempty(tau1) + tau1 = 4; +end +if isempty(kmax) + kmax = 14; +end +if isempty(rho) + rho = sqrt(2); +end + +if tau1*rho^(kmax-1)>tau0 + error('The inputs must satisfy: TAU1*RHO^(KMAX-1)>TAU0') +end +if tau1<0 + error('TAU1 must be positive') +end +if tau0<0 + error('TAU0 must be positive') +end +if kmax<1 || floor(kmax)~=kmax + error('KMAX must be an integer (weakly) larger than 1.') +end +if rho<0 + error('RHO must be positive') +end + +if ndims(data)==2 + [T,K] = size(data); + temp = zeros(K,K,T); + for t=1:T + temp(:,:,t) = data(t,:)'*data(t,:); + end + data = temp; +else + K = size(data,1); + T = size(data,3); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +tauks = tau1*rho.^((1:kmax)-1); +w= 1-log(tauks)/log(tau0); +w=w/sum(w); +Ht = zeros(K,K,T); +Httilde = zeros(K,K,T); + + +for k=1:kmax + tauk = tauks(k); + mu = exp(-1/tauk); + % back casting + endPoint = max(min(floor(log(.01)/log(mu)),T),k); + weights = (1-mu).*mu.^(0:endPoint-1); + weights = weights/sum(weights); + backCast = zeros(K); + for i=1:endPoint + backCast = backCast + weights(i)*data(:,:,i); + end + Httilde(:,:,1) = backCast; + + for t=2:T + Httilde(:,:,t) = mu*Httilde(:,:,t-1) + (1-mu)*data(:,:,t-1); + end + Ht = Ht + w(k) * Httilde; +end + + +if nargout>1 + weights = zeros(T,T); + for k=1:kmax + tauk = tauks(k); + mu = exp(-1/tauk); + weightMatrix = [mu.^(0:T-1)' zeros(T,T-1)]; + weightMatrix(T,T) = (1-mu); + for j=1:(T-2); + weightMatrix(T,T-j) = mu * weightMatrix(T,T-j+1); + end + for t=2:T-1 + weightMatrix(t,2:t) = weightMatrix(T,T+(-t+2:0)); + end + weights = weights + w(k) * weightMatrix; + end +end + + + + + diff --git a/multivariate/scalar_vt_vech.m b/multivariate/scalar_vt_vech.m new file mode 100644 index 0000000..77f49e7 --- /dev/null +++ b/multivariate/scalar_vt_vech.m @@ -0,0 +1,267 @@ +function [parameters, ll, ht, VCV, scores, diagnostics] = scalar_vt_vech(data,dataAsym,p,o,q,startingvals,options) +% Estimation of symmetric and asymmetric scalar multivariate vech ARCH models using variance +% targeting to reduce the number of parameters needing to be estimated simultaneously +% +% USAGE: +% [PARAMETERS,LL,HT,VCV,SCORES,DIAGNOSTICS] = scalar_vt_vech(DATA,DATAASYM,P,O,Q,STARTINGVALS,OPTIONS) +% +% INPUTS: +% DATA - A T by K matrix of zero mean residuals -OR- +% K by K by T array of covariance estimators (e.g. realized covariance) +% DATAASYM - [OPTIONAL] K by K by T array of asymmetric covariance estimators +% P - Positive, scalar integer representing the number of lags of the innovation process +% O - Non-negative scalar integer representing the number of asymmetric lags to include +% Q - Non-negative scalar integer representing the number of lags of conditional covariance +% STARTINGVALS - [OPTIONAL] (p+o+q) x 1 vector of starting values +% OPTIONS - [OPTIONAL] Options to use in the optimization (fminunc) +% +% OUTPUTS: +% PARAMETERS - A p+o+q column vector of parameters. The intercept is reported in DIAGNOSTICS +% LL - The log likelihood at the optimum +% HT - A [K K T] dimension matrix of conditional covariances +% VCV - A numParams^2 square matrix of robust parameter covariances (A^(-1)*B*A^(-1)*t^(-1)) +% SCORES - A T by numParams matrix of individual scores +% +% COMMENTS: +% The conditional variance, H(t), of a scalar variance-targeting vech is modeled +% as follows: +% +% H(t) = (1-alpha(1)+...+alpha(p)-beta(1)-...-beta(q))*C + ... +% alpha(1)*r_{t-1}'*r_{t-1} + ... + alpha(p)*r_{t-p}'*r_{t-p}+... +% gamma(1)*n_{t-1}'*n_{t-1} + ... + gamma(o)*n_{t-p}'*n_{t-p}+... +% beta(1)*H(t-1) +...+ beta(q)*H(t-q) +% +% where n_{t} = r_{t} .* (r_{t}<0) +% +% EXAMPLES: +% Estimation of a Scalar VECH(1,0,1) +% [simulatedData, Ht, pseudoRC] = scalar_vt_vech_simulate(1000, [.02 .04 .95], .01*eye(2), 1, 1, 1, 72); +% parameters = scalar_vt_vech(simulatedData,[],1,0,1) +% Estimation of an asymmetric Scalar VECH(1,1,1) +% parameters = scalar_vt_vech(simulatedData,[],1,1,1) +% Estimation of an asymmetric Scalar VECH(1,1,1) using realized-type data +% asymPseudoRC = zeros(size(pseudoRC)); +% for i = 1:1000 +% asymPseudoRC(:,:,i) = pseudoRC(:,:,i).*(double(simulatedData(i,:)<0)'*double(simulatedData(i,:)<0)); +% end +% parameters = scalar_vt_vech(pseudoRC,asymPseudoRC,1,1,1); + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 10/28/2009 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 3 + o=0; + q=0; + startingvals=[]; + options = []; + case 4 + q=0; + startingvals=[]; + options = []; + case 5 + startingvals=[]; + options = []; + case 6 + options = []; + case 7 + otherwise + error('Between 2 and 6 arguments required.') +end + +%data should be TxK, T>K +if ndims(data)==2 + [t,k]=size(data); + if ~isempty(dataAsym) + error('If DATA is a T by K matrix, DATAASYM must be empty.'); + end + temp = zeros(k,k,t); + dataAsym = zeros(k,k,t); + for i=1:t + temp(:,:,i) = data(i,:)'*data(i,:); + dataAsym(:,:,i) = (data(i,:).*(data(i,:)<0))'*(data(i,:).*(data(i,:)<0)); + end + data = temp; +elseif ndims(data)==3 + [k,m,t] = size(data); + if m~=k + error('DATA must be K by K by T is a 3D array.'); + end + if ~isempty(dataAsym) + if ndims(dataAsym)~=3 + error('DATAASYM must be a 3D array with the same dimensions as DATA'); + end + [k2,m2,t2]=size(dataAsym); + if any([k m t]~=[k2 m2 t2]) + error('DATAASYM must be a 3D array with the same dimensions as DATA'); + end + end +end + +if min(t,k)<2 || tK>1'); +end + +%p, o, q much be non-negative scalars +if length(p)>1 || any(p<1) || floor(p)~=p + error('P must be a positive scalar'); +end +if isempty(o) + o = 0; +end +if length(o)>1 || any(o<0) || floor(o)~=o + error('O must be a non-negative scalar'); +end +if o>0 && isempty(dataAsym) + error('DATAASYM must be non-empty if O>0.') +end + +if isempty(q) + q = 0; +end +if length(q)>1 || any(q<0) || floor(q)~=q + error('Q must be a non-negative scalar'); +end + +% Startingvals must have p+o+q parameters sum(alpha)+kappa*sum(gamma)+sum(beta)<1 +C = mean(data,3); +if o>0 + Casym = mean(dataAsym,3); + kappa = 1 / (max(eig(C^(-0.5)*Casym*C^(-0.5))) + eps); +else + Casym = zeros(k); + kappa = 2; +end +if ~isempty(startingvals) + if size(startingvals,2)>size(startingvals,1) + startingvals = startingvals'; + end + if length(startingvals)<(p+o+q) + error('STARTINGVALS should be a P+O+Q by 1 vector'); + end + %Only validate if provided + A=startingvals(1:p); + G=startingvals(p+1:p+o); + B=startingvals(p+o+1:p+o+q); + if (sum(A)+sum(G)/kappa+sum(B))>=.999998 + error('Weighted sum of STATINGVALUES must be less than 1. See Comments.'); + end + if any(A<0) || any(B<0) || any(G<0) + error('STARTINGVALS must all be nonnegative.'); + end +end + +%Make sure options is a valid option structure +if isempty(options) + options=optimset('fminunc'); + options.Display='iter'; + options.Diagnostics='on'; + options.LargeScale='off'; +end +try + optimset(options); +catch ME + error('OPTIONS is not a valid options structure'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Argument Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Compute the backCast +backCast = zeros(k); +backCastAsym = zeros(k); +tau = max(ceil(sqrt(t)),k); +weights = .06 * .94.^(0:tau); +weights = weights / sum(weights); +for i=1:tau + backCast = backCast + weights(i) * data(:,:,i); + if o>0 + backCastAsym = backCastAsym + weights(i) * dataAsym(:,:,i); + end +end + +%Augment the data with backcasts +[startingvals,lls,output_parameters] = scalar_vt_vech_starting_values(startingvals,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym); %#ok + +% finally to transform the parameters to the unrestricted equivalents +startingvals=scalar_vt_vech_transform(startingvals,p,o,q,kappa); + +[parameters,ll,exitflag,output]=fminunc('scalar_vt_vech_likelihood',startingvals,options,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym,false,true); +%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Estimation Robustification +%%%%%%%%%%%%%%%%%%%%%%%%%%% +if exitflag<=0 && ll1 + [ll,lls,ht]=scalar_vt_vech_likelihood(parameters,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym,false,false); + ll=-ll; +end + +%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Compute the VCV +%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargout>3 + k2 = k*(k+1)/2; + CVech=vech(C); + if o==0 + momentCount = k2; + CasymVech = []; + else + momentCount = 2*k2; + CasymVech=vech(Casym); + end + + A = zeros(momentCount + p + o + q); + A(1:momentCount, 1:momentCount) = - t * eye(momentCount); + jointParameters=[CVech;CasymVech;parameters]; + + % A will be k2 + p + q square + scores = zeros(t,momentCount+p+q); + scoreCount = 1; + for i=1:k + for j=i:k + scores(:,scoreCount) = squeeze(data(j,i,:)); + if o>0 + scores(:,k2+scoreCount) = squeeze(dataAsym(j,i,:)); + end + scoreCount = scoreCount + 1; + end + end + [g,gt] = gradient_2sided(@scalar_vt_vech_likelihood,parameters,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym,false,false); + scores(:,momentCount+1:momentCount+p+o+q) = gt; + A(momentCount+1:momentCount+p+o+q,:) = hessian_2sided_nrows(@scalar_vt_vech_likelihood,jointParameters,p+o+q,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym,true,false); + + A = A/t; + B = covnw(scores); + Ainv = inv(A); + VCV = Ainv*B*Ainv'/t; %#ok + VCV = VCV(momentCount+1:momentCount+p+o+q,momentCount+1:momentCount+p+o+q); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Compute the VCV +%%%%%%%%%%%%%%%%%%%%%%%%%%% +diagnostics.EXITFLAG=exitflag; +diagnostics.ITERATIONS=output.iterations; +diagnostics.FUNCCOUNT=output.funcCount; +diagnostics.MESSAGE=output.message; +diagnostics.kappa=kappa; +alpha = parameters(1:p); +gamma = parameters(p+1:p+o); +beta = parameters(p+o+1:p+o+q); +diagnostics.intercept = C*(1-alpha-beta); +if o>0 + diagnostics.intercept = diagnostics.intercept - gamma*Casym; +end \ No newline at end of file diff --git a/multivariate/scalar_vt_vech_itransform.m b/multivariate/scalar_vt_vech_itransform.m new file mode 100644 index 0000000..e3e46bd --- /dev/null +++ b/multivariate/scalar_vt_vech_itransform.m @@ -0,0 +1,49 @@ +function parameters=scalar_vt_vech_itransform(tparameters,p,o,q,kappa) +% SCALAR_VT_VECH(P,Q) inverse parameter transformation. Used to map parameters +% from the real line to those appropriate for a scalar MVGARCH process. +% Used in the estimation of SCALAR_VT_VECH. +% +% USAGE: +% [PARAMETERS]=scalar_vt_vech_itransform(TPARAMETERS,P,O,Q,KAPPA) +% +% INPUTS: +% TPARAMETERS - Column vector of transformed parameters (-inf,inf) +% P - Positive, scalar integer representing the number of symmetric innovations +% Q - Non-negative, scalar integer representing the number of lags of conditional variance +% +% OUTPUTS: +% PARAMETERS - A 1+p+q column vector of parameters corresponding to +% [alpha(1),...,alpha(p), beta1 ... beta(q)]' +% +% COMMENTS: +% Output parameters will satisfy: +% (1) alpha(i) >= 0 for i = 1,2,...,p +% (2) beta(i) >= 0 for i = 1,2,...,q +% (3) sum(alpha) + sum(beta) < 1 +% +% See also SCALAR_VT_VECH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + +%Upper bound to keep it a bit away from 1 +UB=.999998; +%Make sure there are not inf causing values +tparameters(tparameters>50)=50; +%Map them to [0,1] +parameters=exp(tparameters)./(1+exp(tparameters)); +%Normalize them, starting with the second +scale=UB; +for i=1:p + parameters(i)=parameters(i)*scale; + scale=scale-parameters(i); +end +for i=p+1:p+o + parameters(i)=parameters(i)*scale*kappa; + scale=scale-parameters(i)/kappa; +end +for i=p+o+1:p+o+q + parameters(i)=parameters(i)*scale; + scale=scale-parameters(i); +end diff --git a/multivariate/scalar_vt_vech_jointlikelihood.m b/multivariate/scalar_vt_vech_jointlikelihood.m new file mode 100644 index 0000000..32c210f --- /dev/null +++ b/multivariate/scalar_vt_vech_jointlikelihood.m @@ -0,0 +1,82 @@ +function [ll,lls,ht]=scalar_vt_vech_jointlikelihood(parameters,data,p,q,backCast,isJoint) +% Joint (intercept and dymanics parameters) log likelihood for SCALAR_VT_VECH(P,Q) estimation +% +% USAGE: +% [LL, LLS, HT] = scalar_vt_vech_jointlikelihood(PARAMETERS, DATAAUG, P, Q, K, K2, T) +% +% INPUTS: +% PARAMETERS - A vector of vech GARCH process parameters: [vech(C)' alpha beta]' +% DATAAUG - Augmented (by m back cast values) matrix of mean zero residuals +% P - Positive, scalar integer representing the number of lags of the innovation process +% Q - Non-negative scalar integer representing the number of lags of conditional covariance +% T - Length of the original data +% +% OUTPUTS: +% LL - Minus 1 times the log likelihood +% LLS - Time series of log likelihoods (Also multiplied by -1) +% HT - Time series of conditional covariances +% +% COMMENTS: +% See also SCALAR_VT_VECH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + +k=size(data,2); +k2=k*(k+1)/2; + +C=parameters(1:k2); +C=ivech(C); + +%Parse the parameters +alpha=parameters(k2+1:k2+p); +beta=parameters(k2+p+1:k2+p+q); + +%Compute the constant +const=(1-sum(parameters))*C; + +%Compute the back cast +m=max(p,q); + +%Initialize the covariance +Ht=repmat(C,[1 1 t]); + +%Initialize the log likelihood +ll=0; +lls=zeros(t+m,1); + +%Compute the likelihood constant. +likconst=k*log(2*pi); + +%Perform the recursion +for i=m+1:t+m; + Ht(:,:,i)=const; + for j=1:p + Ht(:,:,i)=Ht(:,:,i)+alpha(j)*(data(i-j,:))'*(data(i-j,:)); + end + for j=1:q + Ht(:,:,i)=Ht(:,:,i)+beta(j)*Ht(:,:,i-j); + end + %Replace these lines to make it work better with poorle conditioned data + %likelihoods(i)=likconst+(log(det(Ht(:,:,i)))+data(i,:)*Ht(:,:,i)^(-1)*data(i,:)'); + + %This is a trick to ensure higher numerical precision + Q=sqrt(diag(Ht(:,:,i))); + R=Ht(:,:,i)./(Q*Q'); + stdresid=data(i,:)./Q'; + lls(i)=likconst+2*sum(log(Q))+log(det(R))+stdresid*R^(-1)*stdresid'; + ll=ll+lls(i); +end + +%Normalize the log likelihood +ll=0.5*ll; + +%If more than one argument out is requested, perform trunctaions and +%normalizations as required +if nargout>1 + lls=0.5*lls(m+1:t+m); + if nargout>2 + Ht=Ht(:,:,m+1:t+m); + end +end diff --git a/multivariate/scalar_vt_vech_likelihood.m b/multivariate/scalar_vt_vech_likelihood.m new file mode 100644 index 0000000..892d7ba --- /dev/null +++ b/multivariate/scalar_vt_vech_likelihood.m @@ -0,0 +1,105 @@ +function [ll,lls,Ht]=scalar_vt_vech_likelihood(parameters,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym,isJoint,estimFlag) +% Log likelihood for SCALAR_VT_VECH(P,O,Q) estimation +% +% USAGE: +% [LL, LLS, HT] = scalar_vt_vech_likelihood(PARAMETERS,DATA,DATAASYM,P,O,Q,C,CASYM,KAPPA,BACKCAST,BACKCASTASYM,ISJOINT,ESTIMFLAG) +% +% INPUTS: +% PARAMETERS - A vector of vech GARCH process parameters: [alpha beta]' or +% [vech(C)' alpha beta]' if ISJOINT +% DATA - K by K by T matrix of covariance innovations +% DATAASYM - K by K by T matrix of asymmetric covariance innovations +% P - Positive, scalar integer representing the number of lags of the innovation process +% O - Non-negative scalar integer representing the number of lags of asymmetric process +% Q - Non-negative scalar integer representing the number of lags of conditional covariance +% C - The unconditional covariance of the data (cov(data) +% CASYM - The unconditional expectation of the asymmetric covariance +% BACKCAST - Back cast value for starting the recursion +% BACKCASTASYM - Back cast value (asymetric terms) for starting the recursion +% ISJOINT - Logical indicating whether the likelihood is the joint across all parameters +% (intercept and dynamics) or is just for the dynamics +% ESTIMFLAG - [OPTIONAL] Flag (0 or 1) to indicate if the function +% is being used in estimation. If it is 1, then the parameters are transformed +% from unconstrained values to constrained by standard garch model constraints +% +% OUTPUTS: +% LL - Minus 1 times the log likelihood +% LLS - Time series of log likelihoods (Also multiplied by -1) +% HT - Time series of conditional covariances +% +% COMMENTS: +% See also SCALAR_VT_VECH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 4 Date: 10/28/2009 + +[k,nothing,T]=size(data); +%If nargin~=7, then we don't need to transform the parameters +base = 0; +if estimFlag + parameters=scalar_vt_vech_itransform(parameters,p,o,q,kappa); + %Parse the parameters +elseif isJoint + k2 = k*(k+1)/2; + base = k2; + C = parameters(1:k2); + C = ivech(C); + if o>0 + Casym = parameters(k2+1:2*k2); + Casym = ivech(Casym); + base = base + k2; + end +end +alpha=parameters(base+(1:p)); +gamma=parameters(base+(p+1:p+o)); +beta=parameters(base+(p+o+1:p+o+q)); +%Compute the constant +const=(1-sum(alpha)-sum(beta))*C; +if o>0 + const = const - sum(gamma)*Casym; +end + +%Initialize the covariance +Ht=repmat(backCast,[1 1 T]); + +%Initialize the log likelihood +lls=zeros(T,1); + +%Compute the likelihood constant. +likconst=k*log(2*pi); + +%Perform the recursion +for t=1:T; + Ht(:,:,t)=const; + for j=1:p + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+alpha(j)*backCast; + else + Ht(:,:,t)=Ht(:,:,t)+alpha(j)*data(:,:,t-j); + end + end + for j=1:o + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+gamma(j)*backCastAsym; + else + Ht(:,:,t)=Ht(:,:,t)+gamma(j)*dataAsym(:,:,t-j); + end + end + for j=1:q + if (t-j)<1 + Ht(:,:,t)=Ht(:,:,t)+beta(j)*backCast; + else + Ht(:,:,t)=Ht(:,:,t)+beta(j)*Ht(:,:,t-j); + end + end + % Replace these lines to make it work better with poorle conditioned data + % likelihoods(i)=likconst+(log(det(Ht(:,:,t)))+data(i,:)*Ht(:,:,t)^(-1)*data(i,:)'); + + %This is a trick to ensure better numerical stability + Q=sqrt(diag(Ht(:,:,t))); + R=Ht(:,:,t)./(Q*Q'); + stdresid=data(:,:,t)./(Q*Q'); + lls(t)=0.5*(likconst+2*sum(log(Q))+log(det(R))+trace(R^(-1)*stdresid)); +end +ll = sum(lls); \ No newline at end of file diff --git a/multivariate/scalar_vt_vech_simulate.m b/multivariate/scalar_vt_vech_simulate.m new file mode 100644 index 0000000..7d5516b --- /dev/null +++ b/multivariate/scalar_vt_vech_simulate.m @@ -0,0 +1,154 @@ +function [simulatedata,ht,pseudorc]=scalar_vt_vech_simulate(t,parameters,c,p,o,q,m) +% Symmetric and Asymmetric SCALAR_VT_VECH(P,O,Q) time series simulation +% +% USAGE: +% [SIMULATEDATA, HT, PSEUDORC] = scalar_vt_vech_simulate(T, PARAMETERS, C, P, O, Q, M) +% +% INPUTS: +% T - Length of the time series to be simulated +% PARAMETERS - a P+O+Q x 1 parameter vector +% [alpha(1) ... alpha(p) gamma(1) ... gamma(o) beta(1) ... beta(q)]'. +% C - K x K matrix containing the intercept +% P - Positive, scalar integer representing the number of symmetric innovations +% O - Non-negative, scalar integer representing the number of asymmetric lags +% Q - Non-negative, scalar integer representing the number of conditional variance lags +% M - [OPTIONAL] Number of ``intradaily'' returns to simulate to pseudo-Realized Covariance +% +% OUTPUTS: +% SIMULATEDATA - A time series with scalar variance-targeting vech covariances +% HT - A [k k t] matrix of simulated conditional covariances +% PSEUDORC - A [k k t] matrix of pseudo-Realized Covariances +% +% COMMENTS: +% The conditional variance, H(t), of a scalar vech is modeled as follows: +% H(t) = C + +% alpha(1)*r_{t-1}'*r_{t-1} + ... + alpha(p)*r_{t-p}'*r_{t-p}+... +% gamma(1)*n_{t-1}'*n_{t-1} + ... + gamma(o)*n_{t-p}'*n_{t-p}+... +% beta(1)*H(t-1) +...+ beta(q)*H(t-q) +% +% where n_{t-1} = r_{t-1} * (r_{t-1}<0). +% +% Pseudo Realized Covariances are simulated by generating m-intra daily returns from a N(0,1/m) +% and computing the Realized Covariance of these. These were used in Patton and Sheppard (2009) +% when evaluating variance and covariance specifications in a Monte Carlo. If M=1, then PSEUDORC +% is just the other product of the SIMULATEDATA. +% +% NOTE: This program generates 2000 more than required to minimize any start-up bias +% +% See also DIAGONAL_BEKK_SIMULATE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 4/1/2004 + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%Check nargin +switch nargin + case 6 + m = 72; + case 7 + % Nothing + otherwise + error('6 or 7 arguments required.'); +end + +%Check t +if ~isscalar(t) && t>0 + error('T must be a positive scalar value.'); +end + +%p, q much be non-negative scalars +if length(p)>1 || any(p<1) || floor(p)~=p + error('P must be a positive scalar'); +end + +if length(o)>1 || any(o<0) || floor(o)~=o + error('O must be a non-negative scalar'); +end + +if length(q)>1 || any(q<0) || floor(q)~=q + error('Q must be a non-negative scalar'); +end + +%Check c +if ndims(c)~=2 || size(c,1)~=size(c,2) || min(eig(c))<0 + error('C must be a positive definite covariance matrix.') +end + +%Check parameters + +if any(parameters<0) || length(parameters)<(p+o+q) + error('All PARAMETERS must be nonnegative and sum to less than 1 (sum(PARAMETERS)<1).'); +end +if (sum(parameters(1:p)) + 0.5*sum(parameters(p+1:p+o)) + sum(parameters(p+o+1:p+o+q)))>=1 + warning('MFEToolbox:Stationarity','PARAMETERS are not compatible with covariance stationary process. Please check HT for problems.') + initialValue = c./(1-.99); +else + initialValue = c./(1-(sum(parameters(1:p)) + 0.5*sum(parameters(p+1:p+o)) + sum(parameters(p+o+1:p+o+q)))); +end +if ~isscalar(m) || floor(m)~=m || m<1 + error('M must be a positive integer.') +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%Set the burnin amount, 2000 is probably reasonable +burnin=2000; +%Up t by the burnin amount +t=t+burnin; + +%Determine K from the size of C +k=length(c); + +% Draw some normal random numbers +intraRandomNums=randn(m*t,k)*sqrt(1/m); +randomNums = cumsum(intraRandomNums); +randomNums = diff([zeros(1,k);randomNums(m:m:m*t,:)]); + +%Determine the back cast length +n=max([p,o,q]); + +%Initialize the random numbers in the back cast range to the unconditional covariance +randomNums(1:n,:)=randomNums(1:n,:)*initialValue^(0.5); + +%Initialize the covariance +ht=repmat(initialValue,[1 1 t]); + +%Initialize the covariance +pseudorc=repmat(initialValue,[1 1 t]); + +%Parse the parameters +alpha=parameters(1:p); +gamma=parameters(p+1:p+o); +beta=parameters(p+o+1:p+o+q); + +%Set the data equal to the randomnums to make things easiest +data = randomNums; +eta = data.*sqrt(0.5); +%Perform the recursion +for i=n+1:t + ht(:,:,i)=c; + for j=1:p + ht(:,:,i)=ht(:,:,i)+alpha(j)*(data(i-j,:)'*data(i-j,:)); + end + for j=1:o + ht(:,:,i)=ht(:,:,i)+gamma(j)*(eta(i-j,:)'*eta(i-j,:)); + end + for j=1:q + ht(:,:,i)=ht(:,:,i)+beta(j)*ht(:,:,i-j); + end + ht(:,:,i) = (ht(:,:,i) + ht(:,:,i)')/2; + ht12 = ht(:,:,i)^(0.5); + r = intraRandomNums((i-1)*m+1:i*m,:)*ht12; + pseudorc(:,:,i) = r'*r; + data(i,:)=data(i,:)*ht12; + eta(i,:) = data(i,:).*(data(i,:)<0); +end +%Truncate the data and the covariance +simulatedata=data(burnin+1:t,:); +pseudorc = pseudorc(:,:,burnin+1:t); +ht=ht(:,:,burnin+1:t); \ No newline at end of file diff --git a/multivariate/scalar_vt_vech_starting_values.m b/multivariate/scalar_vt_vech_starting_values.m new file mode 100644 index 0000000..9ebd005 --- /dev/null +++ b/multivariate/scalar_vt_vech_starting_values.m @@ -0,0 +1,75 @@ +function [startingvals,lls,output_parameters]=scalar_vt_vech_starting_values(startingvals,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym) + +% Perform a grid search to find decent starting values for SCALAR_VT_VECH(P,Q) esimtation. If +% starting values is user supplied (and thus nonempty), does nothing. +% +% USAGE: +% [STARTINGVALS,LLS,OUTPUT_PARAMETERS] = ... +% scalar_vt_vech_starting_values(STARTINGVALS,DATAAUG,P,Q,T,C); +% +% INPUTS: +% STARTINGVALS - A vector of starting values or empty to perform a grid search +% PARAMETERS - A vector of vech GARCH process parameters: [alpha beta]' +% DATA - Augmented (by m back cast values) matrix of mean zero residuals +% P - Positive, scalar integer representing the number of lags of the innovation process +% Q - Non-negative scalar integer representing the number of lags of conditional covariance +% T - Length of the original data +% C - The unconditional covariance of the data (cov(data) +% +% OUTPUTS: +% STARTINGVALS - A vector of starting values (p+q) by 1 +% LLS - A vector of log likelihoods corresponding to OUTPUT_PARAMETERS +% OUTPUT_PARAMETERS - A matrix of alternative starting values, sorted by log likelihood +% +% COMMENTS: +% See also SCALAR_VT_VECH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + +%This code performs a quick grid search of potential starting values +t = size(data,3); +a=[.005 .01 .025 .05]; % The innovation term is usually small +g=[.005 .02 .5 .1]; +apgpb=[.99 .95 .90 .5]; % The smoothing parameter is usually large +count = 1; +params = zeros(length(a)*length(g)*length(apgpb),p+o+q); +for i=1:length(a) + alpha = ones(1,p)*a(i)/p; + for j=1:length(g); + gamma = ones(1,o)*g(j)/o; + for k = 1:length(apgpb) + beta = apgpb(k)-sum(alpha)-sum(gamma)/kappa; + if beta<=apgpb(k)/2; + scale = 0.5 * apgpb(k)/(sum(alpha)+sum(gamma)/kappa); + alpha = alpha*scale; + gamma = gamma*scale; + beta = apgpb(k)-sum(alpha)-sum(gamma)/kappa; + % Reduce alpha and gamma + end + beta = beta*ones(1,q)/q; + params(count,:) = [alpha gamma beta]; + count = count+1; + end + end +end +params = unique(params,'rows'); +params = params(~all(params==0,2),:); + + + +if isempty(startingvals) + lls=zeros(length(params),1); + %Evaluate the likelihood at each parameter + for i=1:size(params,1) + parameters=params(i,:); + lls(i)=scalar_vt_vech_likelihood(parameters,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym,false,false); + end + [lls,pos]=sort(lls); + output_parameters=params(pos,:); + startingvals=output_parameters(1,:); +else + lls=scalar_vt_vech_likelihood(startingvals,data,dataAsym,p,o,q,C,Casym,kappa,backCast,backCastAsym,false,false); + output_parameters=startingvals; +end diff --git a/multivariate/scalar_vt_vech_transform.m b/multivariate/scalar_vt_vech_transform.m new file mode 100644 index 0000000..d47fdd3 --- /dev/null +++ b/multivariate/scalar_vt_vech_transform.m @@ -0,0 +1,76 @@ +function tparameters=scalar_vt_vech_transform(parameters,p,o,q,kappa) +% SCALAR_VT_VECH(P,Q) parameter transformation. Used to map parameters +% from a scalar MVGARCH process to the real line. Used in the estimation of SCALAR_VT_VECH. +% +% USAGE: +% [TPARAMETERS]=scalar_vt_vech_transform(PARAMETERS,P,O,Q,KAPPA) +% +% INPUTS: +% PARAMETERS - Column parameter vector +% P - Positive, scalar integer representing the number of symmetric innovations +% Q - Non-negative, scalar integer representing the number of lags of conditional variance +% +% OUTPUTS: +% TPARAMETERS - A 1+p+q column vector of transformed parameters corresponding to +% [alpha(1),...,alpha(p), beta1 ... beta(q)]' +% +% COMMENTS: +% Input parameters must satisfy: +% (1) alpha(i) >= 0 for i = 1,2,...,p +% (2) beta(i) >= 0 for i = 1,2,...,q +% (3) sum(alpha) + sum(beta) < 1 +% +% See also SCALAR_VT_VECH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 9/1/2005 + +%Upper bound to keep it a bit away from 1 +UB=.999998; + +alpha=parameters(1:p); +gamma = parameters(p+1:p+o); +beta=parameters(p+o+1:p+o+q); +%Check that the parameters satisfy the necessary constraints +if any(alpha<0) || any(beta<0) || any(gamma<0) || (sum(alpha)+sum(gamma)/kappa+sum(beta))>=UB + error('These do not conform to the necessary set of restrictions to be transformed.') +end + +%Alpha, beta cannot be exactly zero or there will be problems with log() +alpha(alpha<1e-8)=1e-8; +gamma(gamma<1e-8)=1e-8; +beta(beta<1e-8)=1e-8; +%Up the upper bound a small amount to make sure it is satisfied +UB=UB+1e-8*(p+o+q); + +%Set the scale +scale=UB; +%Initialize the transformed parameters +parameters=[alpha;gamma;beta]; +tparameters=[alpha;gamma;beta]; +for i=1:(p) + %Scale the parameters + tparameters(i)=tparameters(i)/scale; + %Use an inverse logistic + tparameters(i)=log(tparameters(i)/(1-tparameters(i))); + %Update the scale + scale=scale-parameters(i); +end +for i=p+1:p+o + %Scale the parameters + tparameters(i)=tparameters(i)/scale/kappa; + %Use an inverse logistic + tparameters(i)=log(tparameters(i)/(1-tparameters(i))); + %Update the scale + scale=scale-parameters(i)/kappa; +end + +for i=p+o+1:p+o+q + %Scale the parameters + tparameters(i)=tparameters(i)/scale; + %Use an inverse logistic + tparameters(i)=log(tparameters(i)/(1-tparameters(i))); + %Update the scale + scale=scale-parameters(i); +end \ No newline at end of file diff --git a/realized/ES_20090817.mat b/realized/ES_20090817.mat new file mode 100644 index 0000000000000000000000000000000000000000..99fb933010568b5c83df03e10cb9daa65c0c0963 GIT binary patch literal 2084778 zcmb4pc~nx*8+T=8t6-buN|{+%nwhx*nwpiVxn;RgT3NXeAt}m|SzpbyMN?BDx7;-| za|K#l$_3na!6XGiMMXqFj%;| z0_mSMH8^8xcouZ_jJ`hT|Fdk^c-bDXVZ(-#|7ut!)9==;PaAyCgQlPMfWGaRGB|Sk zl~-`0o$uw7mk2Mu|4Pf)xWSk!XZb&iZ{Az}S$L&wPoqvLw?yA5IeO)!-SZHSv>mon zg=C@B?1J-2Tjy5iOH-g>kK>o$dhd>UU8&HkY7&+HK-sQ$Xz%a$2fu(GoJl)o!kZI$ zd$UZD-sKEKri3o58ly=Y8SW=^b>|Bb+?Z`!-vMM-T8C-*Yd#$O`i!BRL{?=>+bEWu zMNF+m?3R**abP(g+yLMRm1fVRfsl+S)6oa2FAj=&~Xs7|hl?;~}=t z{XZz)D($Uvr*R}&MrE%M>NK;GueqsYZhfir2BhpF>vd%Gv^{OFYzVR%v-)tpl*`z$ 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zVTh`$rk_L`<-NGaT!-E#&3Uh(h(M6MOEk@d8(|5oh%`df4rgPm#~4QD-AfavbF({| z3J~K+m$k*sK(j`<9skJ#YR-pr6qEj=wUIxT2(5<1RrvcOZ)^9K_A8WfbGvCtO#eC{oG)~0 zbW3d7-8XW^=$xrwvLk(`FPfTd!|)cmqu;0llW;6-Xeu~)tiAe3Xrta+Dwj9$rWEgL zOnyeBN$zrf=Ws(vZ8u)|6>T0xF8rB~G? zOp=t@gezlLMSX`SREos*D+P7g{cQyA%yLG7xYP5ZJ`nha{#STFKr(=f0{{H~fIr;f zkMlqLTR>6f?*M;qQ~pEo=eY$ObAM@C{#Ehsy_o5OW&i$qK@~ir<^_oA`uV4JG{!8`d zSA<`y7k?tq;Qe91Kh-k+1LtpBB7dTQ+iOVyfdAMa`BnYbh3uaIh2(!THlK;?=!!m3=G)K003n04FT+_M9e>*{U3L1Ei3>4 literal 0 HcmV?d00001 diff --git a/realized/realized_bipower_variation.m b/realized/realized_bipower_variation.m new file mode 100644 index 0000000..ad66d3b --- /dev/null +++ b/realized/realized_bipower_variation.m @@ -0,0 +1,196 @@ +function [bv,bvSS,bvDebiased,bvSSDebiased]=realized_bipower_variation(price,time,timeType,samplingType,samplingInterval,skip,subsamples) +% Computes bipower variation (BPV), skip-k bipower variation and subsample verisons of these +% +% USAGE: +% [BV,BVSS,BVD,BVSSD] = realized_bipower_variation(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL,SKIP,SUBSAMPLES) +% +% INPUTS: +% PRICE - m by 1 vector of high frequency prices +% TIME - m by 1 vector of times where TIME(i) corresponds to PRICE(i) +% TIMETYPE - String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight on the first day. +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the other types and can be +% applied to data from more than one calendar day +% SAMPLINGTYPE - String describing the type of sampling to use when +% filtering PRICE +% 'CalendarTime' - Sample in calendar time using observations separated by +% SAMPLINGINTERVAL seconds +% 'CalendarUniform' - Sample in calendar time using SAMPLINGINTERVAL +% observations spread uniformly between TIME(1) and TIME(m) +% 'BusinessTime' - Sample in business (tick) time using observation separated +% by SAMPLINGINTERVAL ticks +% 'BusinessUniform' - Sample in business (tick) time using observations +% uniformly spaced in business time. +% 'Fixed' - Sample at specific points in time. When using fixed, +% SAMPLINGINTERVAL must be a n by 1 vector of times with the same TIMETYPE +% as TIME (i.e. seconds if TIME is in seconds) +% SAMPLINGINTERVAL - Scalar integer or n by 1 vector whose meaning depends on the selected SAMPLINGTYPE +% SKIP - [OPTIONAL] Non-negative integer indicating number of return to skip with computing BPV. +% The skip-k BPV is |r_m||r_{m-1-k}| so when k=0 the usual BPV estimator is +% produced. Defulat value is 0. +% SUBSAMPLES - [OPTIONAL] Scalar integer indicating the number of subsample BPV estimators +% to average with the original BPV. Subsample BPV are based on prices +% uniformly spaced between the times (Calendar sampling) or ticks (Business +% sampling). SUBSAMPLES=1 will compute asubsample BPV using the mid-point +% of the price sample points, 2 will use 1/3 and 2/3, and so on. In general +% this number should be small so the subsample estimators will be "sparse". +% +% OUTPUTS: +% BV - Bipower variation estimate +% BVSS - Bipower variation including subsample averaging +% BVD - Debiased version of bipower variation equal to BV times m/(m-SKIP-1) where m +% is the number of returns used to compute BV +% BVSSD - Debiased version of subsampled bipower variation +% +% COMMENTS: +% Skip-k BPV will have a small downward bias of the order (N-k)/N where N is the number of returns +% used in computing the BPV when there are no jumps in the price. If k is large relative to N +% this bias may be worth correcting. +% +% EXAMPLE: +% % 5-minute bipower variation using wall time returns and fixed increments +% fixedInterval = seconds2wall(wall2seconds(93000):300:wall2seconds(160000)); +% BV = realized_bipower_variation(PRICE,TIME,'wall','Fixed',fixedInterval) +% +% % 10-tick bipower variation +% BV = realized_bipower_variation(PRICE,TIME,'wall','BusinessTime',10) +% +% % 5-minute skip-1 bipower varation +% fixedInterval = seconds2wall(wall2seconds(93000):300:wall2seconds(160000)); +% [BV,BVSS] = realized_bipower_variation(PRICE,TIME,'wall','Fixed',fixedInterval,1) +% +% % 5-minute realized variance with subsampling every minute +% fixedInterval = seconds2wall(wall2seconds(93000):300:wall2seconds(160000)); +% BV = realized_bipower_variation(PRICE,TIME,'wall','Fixed',fixedInterval,0,5) +% +% +% See also REALIZED_VARIANCE, REALIZED_QUARTICITY, REALIZED_KERNEL, REALIZED_QUANTILE_VARIANCE, +% REALIZED_RANGE, REALIZED_PRICE_FILTER, REALIZED_KERNEL_WEIGHTS + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin<5 || nargin>7 + error('Five to Seven inputs required.') +end +if size(price,2)>size(price,1) + price=price'; +end +if size(price,2)>1 + error('PRICE must be a m by 1 vector.') +end +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + error('TIME must be sorted and increasing') +end +if size(time,2)>1 || length(time)~=length(price) + error('TIME must be a m by 1 vector.') +end +% Inserted to protect against inputing integer times +timeCase = whos('time'); +if ~strcmp(timeCase.class,'double') + time = double(time); +end + +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','unit'}) + error('TIMETYPE must be one of ''wall'', ''seconds'' or ''unit''.'); +end +samplingType=lower(samplingType); +if ~ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + error('SAMPLINGTYPE must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.'); +end + +m=size(price,1); +t0=time(1); +tT=time(m); +if ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform'}) + % Must be a scalar integer if timeType is seconds or wall + if ismember(timeType,{'wall','seconds'}) + if ~isscalar(samplingInterval) || floor(samplingInterval)~=samplingInterval || samplingInterval<1 + error('SAMPLINGINTERVAL must be a positive integer for the SAMPLINGTYPE selected when using ''wall'' or ''seconds'' as TIMETYPE.') + end + else + if ~isscalar(samplingInterval) || samplingInterval<0 + error('SAMPLINGINTERVAL must be a positive value for the SAMPLINGTYPE selected when using ''unit'' as TIMETYPE.') + end + end +else + if size(samplingInterval,2)>size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + if ~(any(samplingInterval>=t0) && any(samplingInterval<=tT)) + error('At least one sampling interval must be between min(TIME) and max(TIME) when using ''Fixed'' as SAMPLINGTYPE.') + end + if any(diff(samplingInterval)<=0) + error('When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.') + end +end + +if nargin>=6 && ~isempty(skip) + if ~isscalar(skip) || skip<0 || floor(skip)~=skip + error('SKIP must be a non-negative scalar.') + end +else + skip = 0; +end + +if nargin==7 && ~isempty(subsamples) + if ~isscalar(subsamples) || subsamples<0 || floor(subsamples)~=subsamples + error('SUBSAMPLES must be a non-negative scalar.') + end +else + subsamples = 1; +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +% Convert times to unit if not already unit +if ~strcmp(timeType,'unit') + [time,~,~,samplingInterval]=realized_convert2unit(time,timeType,samplingType,samplingInterval); +end +% Since everything is converted to unit, set timeType to unit +timeType='unit'; + +% Filter prices and compute the RV +logPrice = log(price); +filteredLogPrice = realized_price_filter(logPrice,time,timeType,samplingType,samplingInterval); +returns = diff(filteredLogPrice); +m = length(returns); +if (m-1-skip)<1 || (2+skip)>m + error('The value of SKIP is too large for the sampling method used. SKIP should be small relative to the number of prices computed using the chosen sampling method.') +elseif (skip/m)>.1 + warning('oxfordRealized:skipTooLarge',['The value chosen for skip is large relative to the number of prices returned for the chosen \n'... + 'SAMPLINGTYPE and SAMPLINGINTERVAL - (skip / #returns) > .1 indicating more than 10%% of the returns \n'... + 'are being dropped. Interpret the results with caution.']); +end + +bv= (pi/2) * abs(returns(1:m-1-skip))'*abs(returns(2+skip:m)); +biasScale = (m-1-skip) / m ; +bvDebiased = bv / biasScale; + +subsampledLogPrices = realized_subsample(logPrice,time,timeType,samplingType,samplingInterval,subsamples); +bvs = zeros(subsamples,1); +totalCount = 0; +for i=1:subsamples + returns = diff(subsampledLogPrices{i}); + m = length(returns); + bvs(i) = (pi/2) * abs(returns(1:m-1-skip))'*abs(returns(2+skip:m)); + if i==1 + baseCount = m-1-skip; + end + totalCount = totalCount + m-1-skip; +end +bvSS = sum(bvs) * (baseCount / totalCount); +bvSSDebiased = bvSS / biasScale; diff --git a/realized/realized_compute_median.m b/realized/realized_compute_median.m new file mode 100644 index 0000000..96249ca --- /dev/null +++ b/realized/realized_compute_median.m @@ -0,0 +1,122 @@ +function [medianPrice,medianTime,totalVol,nObs] = realized_compute_median(price,time,volume) +% Computes the median price at each time stamp for a vector of prices which may have multiple +% observations with the same time stamp. +% +% USAGE: +% [MEDIANPRICE,MEDIANTIME,TOTALVOL,NOBS] = realized_compute_median(PRICE,TIME,VOLUME) +% +% INPUTS: +% PRICE - m by 1 vector of high frequency prices +% TIME - m by 1 vector of times where TIME(i) corresponds to PRICE(i), sorted in +% ascending order +% VOLUME - [OPTIONAL] m by 1 vector of transaction volumes or bid/ask size. If omitted +% TOTALVOLUME will be a vector of 0's. +% +% OUTPUTS: +% MEDIANPRICE - n by 1 vector of median prices where n is the number of unique elements of TIME +% MEDIANTIME - n by 1 vector of time stamps corresponding to MEDIANPRICE +% TOTALVOLUME - n by 1 vector capturing the total volume at each time stamp +% NOBS - n by 1 vector indicating number of prices at each element of MEDIANTIME +% +% COMMENTS: +% This is a helper function for most of the Realized toolkit. Most function in the Realized +% toolkit expect time stamps to be unique. Median price is a reasonable and fairly robust (to +% noise) method of computing a unique price for each time stamp. + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 2 Date: 6/12/2011 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% InputChecking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin<2 || nargin>3 + error('Six or seven inputs required.') +end +if size(price,2)>size(price,1) + price=price'; +end +if size(price,2)>1 + error('PRICE must be a m by 1 vector.') +end +m = size(price,1); + +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + error('TIME must be sorted and increasing') +end +if size(time,2)>1 || length(time)~=m + error('TIME must be a m by 1 vector.') +end +time = double(time); + +if nargin == 3 + if size(volume,2)>size(volume,1) + volume=volume'; + end + if size(volume,2)>1 || length(volume)~=m + error('VOLUME must be a m by 1 vector.') + end +else + volume = zeros(m,1); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Make sure time and volume are double since I store it was uint32 +time = double(time); +volume = double(volume); + +% Quickly find the time change points +pl = find(diff(time)); +pl = [1;pl+1;length(time)+1]; + +% Get the number of observations +N = length(pl); + +% Pre-allocatte +medianPrice = zeros(N-1,1); +medianTime = time(pl(1:N-1)); +totalVol = zeros(N-1,1); +nObs = zeros(N-1,1); + +% Loop over unique sizes, with special cases for 1 and 2 +[sizes,~,ind]=unique(diff(pl)); +for i=1:length(sizes) + j=find(ind==i); + loc = bsxfun(@plus,pl(j),0:sizes(i)-1)'; + switch sizes(i) + case 1 + medianPrice(j) = price(pl(j)); + totalVol(j) = volume(pl(j)); + case 2 + medianPrice(j) = (price(pl(j)) + price(pl(j)+1))/2; + otherwise + sortedPrice = sort(price(loc)); + if mod(sizes(i),2)==0 + medianPrice(j) = mean(sortedPrice([sizes(i)/2;sizes(i)/2+1],:))'; + else + medianPrice(j) = sortedPrice(ceil(sizes(i)/2),:)'; + end + end + totalVol(j) = sum(volume(loc))'; + nObs(j) = sizes(i); +end + +% Old, slower method +% Loop +% singleton = pldiff==1; +% medianPrice(singleton) = price(pl(singleton)); +% totalVol(singleton) = volume(pl(singleton)); +% nObs(singleton) = 1; +% notSingleton = find(~singleton); +% +% for i=1:length(notSingleton) +% j = notSingleton(i); +% medianPrice(j) = median(price(pl(j):pl(j+1)-1)); +% totalVol(j) = sum(volume(pl(j):pl(j+1)-1)); +% nObs(j) = pl(j+1)-pl(j)+1; +% end diff --git a/realized/realized_convert2unit.m b/realized/realized_convert2unit.m new file mode 100644 index 0000000..23ec849 --- /dev/null +++ b/realized/realized_convert2unit.m @@ -0,0 +1,133 @@ +function [time,time0,time1,samplingInterval]=realized_convert2unit(time,timeType,samplingType,samplingInterval) +% Helper function that converts wall and seconds times to unit times, assigning +% 0 to the smallest time and 1 to the largest. +% +% USAGE: +% [TIME,TIME0,TIME1,SAMPLINGINTERVAL]=realized_convert2unit(TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL) +% +% INPUTS: +% TIME - m by 1 vector of times where TIME(i) corresponds to +% PRICE(i). Must be either wall time or measurements in seconds +% TIMETYPE - String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight on +% the first day. +% SAMPLINGTYPE - String describing the type of sampling to use when +% filtering PRICE +% 'CalendarTime' - Sample in calendar time using +% observations separated by SAMPLINGINTERVAL +% seconds. +% 'CalendarUniform' - Sample in calendar time using +% SAMPLINGINTERVAL observations spread uniformly +% between TIME(1) and TIME(m) +% 'BusinessTime' - Sample in business (tick) time +% using observation separated by SAMPLINGINTERVAL +% ticks +% 'BusinessUniform' - Sample in business (tick) +% time using observations uniformly spaced in +% business time. +% 'Fixed' - Sample at specific points in time. When +% using fixed, SAMPLINGINTERVAL must be a n by 1 vector +% of times with the same TIMETYPE as TIME (i.e. +% seconds if TIME is in seconds) +% SAMPLINGINTERVAL - Scalar integer or n by 1 vector whose meaning depends on the +% selected SAMPLINGTYPE +% +% OUTPUTS: +% TIME - The original times mapped to 0-1 +% TIME0 - The base time in original format. Required to invert the transformation. +% TIME0 - The final time in original format. Required to invert the transformation. +% SAMPLINGINTERVAL - The sampling interval converted to the unit scale. +% If SAMPLINGYPE is not 'CalendarTime' or 'Fixed', SAMPLINGINTERVAL +% is not altered +% +% COMMENTS: +% +% See also REALIZED_KERNEL, REALIZED_PRICE_FILTER, REALIZED_VARIANCE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=4 + error('Four inputs required.') +end +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + error('TIME must be sorted and increasing') +elseif any(diff(time)==0) + warning('oxfordRealized:realizedPriceFilter','TIME contains multiple entries with the same value. This creates an ambiguity and FILTEREDPRICE will contain the last price if TIME does not only unique elements.') +end +if size(time,2)>1 || length(time)~=length(time) + error('TIME must be a m by 1 vector.') +end +% Inserted to protect against inputing integer times + time = double(time); + +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds'}) + error('TIMETYPE must be one of ''wall'' or ''seconds''.'); +end +samplingType=lower(samplingType); +if ~ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + error('SAMPLINGTYPE must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.'); +end + +m=size(time,1); +t0Original=time(1); +tTOriginal=time(m); +if ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform'}) + if (~isscalar(samplingInterval) || floor(samplingInterval)~=samplingInterval || samplingInterval<1) + error('SAMPLINGINTERVAL must be a positive integer for the SAMPLINGTYPE selected.') + end +else + if size(samplingInterval,2)>size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + if ~(any(samplingInterval>=t0Original) && any(samplingInterval<=tTOriginal)) + error('At least one sampling interval must be between min(TIME) and max(TIME) when using ''Fixed'' as SAMPLINGTYPE.') + end + if any(diff(samplingInterval)<=0) + error('When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.') + end +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +if strcmp(samplingType,'fixed') + time0 = min(samplingInterval); + time1 = max(samplingInterval); +else + time0 = min(time); + time1 = max(time); +end +if strcmp(timeType,'wall') + time = wall2unit(time,time0,time1); +elseif strcmp(timeType,'seconds') + time = seconds2unit(time,time0,time1); +end +% If fixed convert these times as well +if strcmp(samplingType,'fixed') + if strcmp(timeType,'wall') + samplingInterval = wall2unit(samplingInterval,time0,time1); + elseif strcmp(timeType,'seconds') + samplingInterval = seconds2unit(samplingInterval,time0,time1); + end +end +if strcmp(samplingType , 'calendartime') + if strcmp(timeType,'wall') + timeBase = wall2seconds([time0 time1]); + samplingInterval = samplingInterval/diff(timeBase); + elseif strcmp(timeType,'seconds') + samplingInterval = samplingInterval/(time1-time0); + end +end + diff --git a/realized/realized_covariance.m b/realized/realized_covariance.m new file mode 100644 index 0000000..4593fcf --- /dev/null +++ b/realized/realized_covariance.m @@ -0,0 +1,216 @@ +function [rc,rcSS]=realized_covariance(varargin) +% Estimates Realized Covariance and subsampled Realized Variance +% +% USAGE: +% [RC,RCSS] = realized_covariance(PRICE01,TIME01,PRICE02,TIME02,...,PRICEN,TIMEN,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL,SUBSAMPLES) +% +% INPUTS: +% PRICE01 - m01 by 1 vector of high frequency prices +% TIME01 - m01 by 1 vector of times where TIME01(i) corresponds to PRICE01(i) +% PRICE02 - m02 by 1 vector of high frequency prices +% TIME02 - m02 by 1 vector of times where TIME02(i) corresponds to PRICE02(i) +% [N - 3 price-time pairing as required, where N can be any integer] +% PRICEN - mN by 1 vector of high frequency prices +% TIMEN - mN by 1 vector of times where TIMEN(i) corresponds to PRICEN(i) +% TIMETYPE - String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight on the first day. +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the other types and can be +% applied to data from more than one calendar day +% SAMPLINGTYPE - String describing the type of sampling to use when filtering PRICE01. Once +% PRICE01 is filtered, all other prices are filtered using the same +% time-stamps as the filtering proceedure produces for PRICE01. +% 'CalendarTime' - Sample in calendar time using +% observations separated by SAMPLINGINTERVAL seconds +% 'CalendarUniform' - Sample in calendar time using +% SAMPLINGINTERVAL observations spread uniformly +% between TIME(1) and TIME(m) +% 'Fixed' - Sample at specific points in time. When +% using fixed, SAMPLINGINTERVAL must be a n by 1 vector +% of times with the same TIMETYPE as TIME (i.e. +% seconds if TIME is in seconds) +% SAMPLINGINTERVAL - Scalar integer or n by 1 vector whose meaning depends on the +% selected SAMPLINGTYPE +% SUBSAMPLES - [OPTIONAL] Scalar integer indicating the number of subsample realized +% variance estimators to average with the original realized variance. +% Subsample realized variances are based on prices uniformly spaced between +% the times. SUBSAMPLES=1 will compute a subsample realized variance using +% the mid-point of the price sample points, 2 will use 1/3 and 2/3, and so +% on. In general this number should be small so the subsample estimators +% will be "sparse". +% +% OUTPUTS: +% RC - Realized covariance estimate +% RKSS - Realized covariance including subsample averaging. If SUBSAMPLE = 0 or is +% omitted, RCSUBSAMPLE = RC +% +% COMMENTS: +% +% EXAMPLES: +% +% See also REALIZED_KERNEL, REALIZED_HAYASHI_YOSHIDA, REALIZED_VARIANCE, +% REALIZED_QUANTILE_VARIANCE, REALIZED_RANGE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 7/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Need to parse teh varargin +Q = length(varargin); +if Q<5 + error('At least 5 minutes required.') +end +% Determin number of price, either Q-2 or Q-3 must be a time type +if ismember(varargin{Q-2},{'wall','seconds','unit'}) + % Then the number of inputs is (Q-3)/2 + k = (Q-3)/2; +elseif ismember(varargin{Q-3},{'wall','seconds','unit'}) % This is case where subsample is asked for + k = (Q-4)/2; +else + error('Inputs are not valid. The final arguments must be either TIMETYPE, SAMPLINGTYPE and SAMPLINGINTERVAL or TIMETYPE, SAMPLINGTYPE, SAMPLINGINTERVAL and SUBSAMPLES if using subsampling.') +end + +% Parse price and time, make sure they are compatible with one another +price = cell(k,1); +time = cell(k,1); +% Gether the times and prices into cell arrays +for i=1:k + price{i} = varargin{(i-1)*2+1}; + time{i} = double(varargin{i*2}); + if size(price{i},2)>size(price{i},1) + price{i}=price{i}'; + end + if size(time{i},2)>size(time{i},1) + time{i}=time{i}'; + end + if size(price{i},1)~=size(time{i},1) + error(['Problem with PRICE' num2str(k) ' and TIME' num2str(k) '. Their lengths are not compatible or they are not column vectors.']) + end + if any(diff(time{i})<0) + error(['TIME' num2str(k) ' must be sorted and increasing.']) + end + time{i} = double(time{i}); +end +timeType = varargin{2*k+1}; +samplingType = varargin{2*k+2}; +samplingInterval = varargin{2*k+3}; + +if Q==(2*k+4) + subsamples = varargin{2*k+4}; +else + subsamples = 0; +end + +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','unit'}) + error('TIMETYPE must be one of ''wall'', ''seconds'' or ''unit''.'); +end + +samplingType=lower(samplingType); +if ~ismember(samplingType,{'calendartime','calendaruniform','fixed'}) + error('SAMPLINGTYPE must be one of ''CalendarTime'', ''CalendarUniform'' or ''Fixed''.'); +end + + +if ismember(samplingType,{'calendartime','calendaruniform'}) + % Must be a scalar integer if timeType is seconds or wall + if ismember(timeType,{'wall','seconds'}) + if ~isscalar(samplingInterval) || floor(samplingInterval)~=samplingInterval || samplingInterval<1 + error('SAMPLINGINTERVAL must be a positive integer for the SAMPLINGTYPE selected when using ''wall'' or ''seconds'' as TIMETYPE.') + end + else + if ~isscalar(samplingInterval) || samplingInterval<0 + error('SAMPLINGINTERVAL must be a positive value for the SAMPLINGTYPE selected when using ''unit'' as TIMETYPE.') + end + end +else + if size(samplingInterval,2)>size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + for i = 1:k + m=size(price{i},1); + t0=time{i}(1); + tT=time{i}(m); + if ~(any(samplingInterval>=t0) && any(samplingInterval<=tT)) + error(['At least one sampling interval must be between min(TIME' num2str(k) ' ) and max(TIME' num2str(k) ') when using ''Fixed'' as SAMPLINGTYPE.']) + end + end + if any(diff(samplingInterval)<=0) + error('When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.') + end +end + +if ~isempty(subsamples) + if ~isscalar(subsamples) || subsamples<0 || floor(subsamples)~=subsamples + error('SUBSAMPLES must be a non-negative scalar.') + end +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + +% Convert times to unit if not already unit +if ~strcmp(timeType,'unit') + [time{1},time0,time1,samplingInterval]=realized_convert2unit(time{1},timeType,samplingType,samplingInterval); + for j=2:k + % This is custom function to map to the unit interval according to the first price + time{j}=realized_multivariate_convert2unit(time{j},timeType,time0,time1); + end +end + +% Filter prices and compute the RC +[filteredPrice(:,1),filteredTimes] = realized_price_filter(price{1},time{1},'unit',samplingType,samplingInterval); +% filteredTimes turns a problem with uniform times into a problem with +% fixed times +n = size(filteredPrice,1); +filteredPrice = [filteredPrice zeros(n,k-1)]; +for j=2:k + filteredPrice(:,j) = realized_price_filter(price{j},time{j},'unit','fixed',filteredTimes); +end + +returns = diff(log(filteredPrice)); +rc=returns' * returns; +adjFactor = length(returns); + + +subsampledLogPrices = cell(k,1); +for j=1:k + logPrice = log(price{j}); + subsampledLogPrices{j} = realized_subsample(logPrice,time{j},timeType,'fixed',filteredTimes,subsamples); +end + +rcs = zeros(k,k,subsamples); +totalCount = 0; +for i=1:subsamples + m = size(subsampledLogPrices{1}{i},1); + allLogPrices = zeros(m,k); + for j=1:k + allLogPrices(:,j) = subsampledLogPrices{j}{i}; + end + + returns = diff(allLogPrices); + if i==1 + baseCount = size(returns,1); + end + totalCount = totalCount + size(returns,1); + rcs(:,:,i) = (returns' * returns); +end +rcSS = sum(rcs,3) * (baseCount / totalCount); + + + +function time=realized_multivariate_convert2unit(time,timeType,time0,time1) +% Quick conversion function +if strcmp(timeType,'wall') + time = wall2unit(time,time0,time1); +elseif strcmp(timeType,'seconds') + time = seconds2unit(time,time0,time1); +end + diff --git a/realized/realized_hayashi_yoshida.m b/realized/realized_hayashi_yoshida.m new file mode 100644 index 0000000..93a827e --- /dev/null +++ b/realized/realized_hayashi_yoshida.m @@ -0,0 +1,311 @@ +function rchy = realized_hayashi_yoshida(priceA,timeA,priceB,timeB,timeType,samplingType,samplingInterval,overlap) +% Computed the Hayashi-Yoshida estimator of quadratic covariation, and allows for +% the empirical-performance motivated K-lead-and-lag version similar to Drost and Nijman (1997). +% +% USAGE: +% [RCHY] = realized_hayashi_yoshida_(PRICEA,TIMEA,PRICEB,TIMEB,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL,OVERLAP) +% +% INPUTS: +% PRICEA - mA by 1 vector of high frequency prices +% TIMEA - mA by 1 vector of times where TIMEB(i) corresponds to PRICEA(i) +% PRICEA - mB by 1 vector of high frequency prices +% TIMEA - mB by 1 vector of times where TIMEB(i) corresponds to PRICEB(i) +% TIMETYPE - String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS, e.g. 101543 or 153217 +% 'seconds' Time measures in seconds past midnight. +% TIME must satisfy 0<=TIME<86400 +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the +% other types and can be applied to data from more +% than one calendar day +% SAMPLINGTYPE - String describing the type of sampling to use when +% filtering PRICE +% 'CalendarTime' - Sample in calendar time using +% observations separated by SAMPLINGINTERVAL +% seconds. If TIMETYPE is 'unit', +% SAMPLINGINTERVAL must be between 0 and 1 and +% represents the fraction of the sample to skip +% when sampling. +% 'CalendarUniform' - Sample in calendar time using +% SAMPLINGINTERVAL observations spread uniformly +% between TIME(1) and TIME(m) +% 'BusinessTime' - Sample in business (tick) time +% using observation separated by SAMPLINGINTERVAL +% ticks +% 'BusinessUniform' - Sample in business (tick) +% time using observations uniformly spaced in +% business time. +% 'Fixed' - Sample at specific points in time. When +% using fixed, SAMPLINGINTERVAL must be a n by 1 vector +% of times with the same TIMETYPE as TIME (i.e. +% seconds if TIME is in seconds) +% SAMPLINGINTERVAL - Scalar integer or n by 1 vector whose meaning depends on the +% selected SAMPLINGTYPE +% OVERLAP - Number of ticks to overlap when computing the HY estimator. The original HY +% estimator uses 0, which corresponds to the maximum likelihood estimator for +% price processes whose observation times are driven by independent Poisson +% processes. Empirically this estimator performs poorly because prices are +% not a vector semi-martingale and using a larger number of lags can alleviate +% this problem. +% +% OUTPUTS: +% RCHY - The K-lead-and-lag Hayashi-Yoshida covariance estimator +% +% COMMENTS: +% Filtering the price in calendar time allow the creation of a Hayashi-Yoshida corrected +% calendar-time sampled realized covariance. The value in SAMPLINGTYPE is applied to price A and +% then the realized HY estimator is computed using the filtered price of A and the filtered times +% of A, and all observations of B. Price filtering is done using realized_price_filter +% +% EXAMPLES: +% % Standard use with all prices with wall time prices +% RCHY = realized_hayashi_yoshida(PRICEA,TIMEA,PRICEB,TIMEB,'wall','BusinessTime',1,0) +% +% % 10 lead and lag RCHY with all prices with wall time prices +% RCHY = realized_hayashi_yoshida(PRICEA,TIMEA,PRICEB,TIMEB,'wall','BusinessTime',1,10) +% +% % 1-minute realized covariance with a HY correction +% RCHY = realized_hayashi_yoshida(PRICEA,TIMEA,PRICEB,TIMEB,'wall','CalendarTime',60,0) +% +% See also REALIZED_MULTIVARIATE_KERNEL, REALIZED_COVARIANCE, REALIZED_KERNEL, REALIZED_VARIANCE, +% REALIZED_RANGE, REALIZED_QUANTILE_VARIANCE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin<7 || nargin>8 + error('Seven or eight inputs required.') +end +if size(priceA,2)>size(priceA,1) + priceA=priceA'; +end +if size(priceA,2)>1 + error('PRICEA must be a m by 1 vector.') +end +if size(timeA,2)>size(timeA,1) + timeA=timeA'; +end +if any(diff(timeA)<0) + error('TIMEA must be sorted and increasing') +elseif any(diff(timeA)==0) + warning('oxfordRealized:realizedPriceFilter','TIMEA contains multiple entries with the same value. This creates an ambiguity and FILTEREDPRICE will contain the last price if TIMEA does not only unique elements.') +end +if size(timeA,2)>1 || length(timeA)~=length(priceA) + error('TIMEA must be a m by 1 vector.') +end +% Inserted to protect against inputing integer times +timeA = double(timeA); +if size(priceB,2)>size(priceB,1) + priceB=priceB'; +end +if size(priceB,2)>1 + error('PRICEB must be a m by 1 vector.') +end +if size(timeB,2)>size(timeB,1) + timeB=timeB'; +end +if any(diff(timeB)<0) + error('TIMEB must be sorted and increasing') +elseif any(diff(timeB)==0) + warning('oxfordRealized:realizedPriceFilter','TIMEB contains multiple entries with the same value. This creates an ambiguity and FILTEREDPRICE will contain the last price if TIMEB does not only unique elements.') +end +if size(timeB,2)>1 || length(timeB)~=length(priceB) + error('TIMEB must be a m by 1 vector.') +end +% Inserted to protect against inputing integer times +timeB = double(timeB); + +% make sure the intersection is non-empty +if ~(min(timeB)size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + if ~(any(samplingInterval>=t0Original) && any(samplingInterval<=tTOriginal)) + error('At least one sampling interval must be between min(TIME) and max(TIME) when using ''Fixed'' as SAMPLINGTYPE.') + end + if any(diff(samplingInterval)<=0) + error('When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.') + end +end + +if strcmp(timeType,'unit') && strcmp(samplingType,'calendartime') + % samplingInterval must be between 0 and 1 + if samplingInterval>1 + error('When TIMETYPE is ''unit'' and SAMPLINGTYPE is ''CalendarTime'', SAMPLINGINTERVAL must also be in ''unit'' terms, and so must be between 0 and 1') + end +end + +if nargin==7 + overlap = 0; +elseif overlap<0 || floor(overlap)~=overlap || max(size(overlap))>1 + error('OVERLAP must be a non-negative integer.') +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +% Price A is the base price, price B is the other price. First sample priceA according to +% samplingType and samplingInterval, then use the actual times of these to estimate the HY +% respecting the value in overlap + +if ~intersectionIsEmpty + % First filter the price + [filteredPriceA,filteredTimeA,actualTimeA] = realized_price_filter(priceA,timeA,timeType,samplingType,samplingInterval); + + % Then call the core routine + rchy = realized_hayashi_yoshida_core(filteredPriceA,actualTimeA,priceB,timeB,overlap); +else + rchy = 0; +end + + + + + +function [rchy,times] = realized_hayashi_yoshida_core(priceA,timeA,priceB,timeB,overlap) +% Core routine for computing the Hayashi-Yoshida estimator of quadratic covariation, and allows for +% the empirical-performance motivated K-lead-and-lag version similar to Drost and Nijman (1997). +% +% USAGE: +% [RCHY,TIMES] = realized_hayashi_yoshida_core(PRICEA,TIMEA,PRICEB,TIMEB,OVERLAP) +% +% INPUTS: +% PRICEA - mA by 1 vector of high frequency prices +% TIMEA - mA by 1 vector of times where TIMEB(i) corresponds to PRICEA(i) +% PRICEA - mB by 1 vector of high frequency prices +% TIMEA - mB by 1 vector of times where TIMEB(i) corresponds to PRICEB(i) +% OVERLAP - [OPTIONA] Number of ticks to overlap when computing the HY estimator. The +% original HY estimator uses 0, which corresponds to the maximum likelihood +% estimator for price processes whose observation times are driven by +% independent Poisson processes. Empirically this estimator performs poorly +% because prices are not a vector semi-martingale and using a larger number +% of lags can alleviate this problem. If omitted OVERLAP = 0. +% +% OUTPUTS: +% RCHY - The K-lead-and-lag Hayashi-Yoshida covariance estimator +% TIMES - A mA by 1 matrix of time stamps contains the times where the prices were +% sampled for computing the returns in the HY estimator. This is mostly for +% diagnostic purposes. +% +% COMMENTS: +% This is a helper function of realized_hayashi_yoshida and does no input checking. In general +% it should not be directly called. +% +% See also REALIZED_MULTIVARIATE_KERNEL, REALIZED_COVARIANCE, REALIZED_KERNEL, REALIZED_VARIANCE, +% REALIZED_RANGE, REALIZED_QUANTILE_VARIANCE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +priceA = log(priceA); +priceB = log(priceB); +timeA = double(timeA); +timeB = double(timeB); +% Price A is the base price, price B is the one which will move + +% First find the first time that B is available before timeA(1). If it is empty then find the first +% timeA(1) which is weakly after the timeB(1) +nA = size(priceA,1); +nB = size(priceB,1); + +if timeA(1)timeB(nB) + % A ends after B, so the easy solution is to project forward the last price B to the + % time of the last A. This will generate a 0 return but makes the algorithm easier. + timeB=[timeB;timeA(nA)]; + priceB=[priceB;priceB(nB)]; + nB = size(priceB,1); +end + + + + +% Initialize the indices for A and B +indexA = 1; +indexB = find(timeB<=timeA(1), 1,'last'); +if overlap>0 + indexB = max(indexB-overlap,1); % Make sure that indexB is >= 1 +end + +% Initialize rchy and the times +rchy = 0; +times = zeros(nA-1,4); +while indexAtimeA(indexA) + indexB = indexB - 1; + end +end diff --git a/realized/realized_kernel.m b/realized/realized_kernel.m new file mode 100644 index 0000000..f020682 --- /dev/null +++ b/realized/realized_kernel.m @@ -0,0 +1,415 @@ +function [rk,rkAdjusted,diagnostics]=realized_kernel(price,time,timeType,samplingType,samplingInterval,options) +% Estimated quadratic variation using Realized Kernels +% +% USAGE: +% [RK,RKADJUSTED,DIAGNOSTICS] = realized_kernel(PRICE) +% [RK,RKADJUSTED,DIAGNOSTICS] = realized_kernel(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL) +% [RK,RKADJUSTED,DIAGNOSTICS] = realized_kernel(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL,OPTIONS) +% +% INPUTS: +% PRICE - m by 1 vector of high frequency prices +% TIME - [OPTIONAL] m by 1 vector of times where TIME(i) corresponds to PRICE(i). +% TIMETYPE - [OPTIONAL] String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS.mmm, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the other types and can be +% applied to data from more than one calendar day +% SAMPLINGTYPE - [OPTIONAL] String describing the type of sampling to use when +% filtering PRICE +% 'CalendarTime' - Sample in calendar time using observations separated by +% SAMPLINGINTERVAL seconds +% 'CalendarUniform' - Sample in calendar time using SAMPLINGINTERVAL +% observations spread uniformly between TIME(1) and TIME(m) +% 'BusinessTime' - Sample in business (tick) time using observation separated +% by SAMPLINGINTERVAL ticks +% 'BusinessUniform' - Sample in business (tick) time using observations +% uniformly spaced in business time. +% 'Fixed' - Sample at specific points in time. When using fixed, +% SAMPLINGINTERVAL must be a n by 1 vector of times with the same TIMETYPE +% as TIME (i.e. seconds if TIME is in seconds) +% SAMPLINGINTERVAL - [OPTIONAL] Scalar integer or n by 1 vector whose meaning depends on the +% selected SAMPLINGTYPE +% OPTIONS - [OPTIONAL] Realized Kernel option structure initialized by calling +% realized_options('Kernel'). See help realized_options for a description of +% available options. +% +% OUTPUTS: +% RK - Realized kernel estimate +% RKADJUSTED - Realized kernel estimate adjusted to recognize that less than the entire sample +% was used to estimate the quadratic variation +% DIAGNOSTICS - Structure of useful diagnostic information. Fields are +% KERNEL - The kernel used in the RK +% BANDWIDTH - Number of lags used in the RK except in the case of an +% infinite lag kernel. +% ADJUSTMENT - De-biasing adjustment for the RK to recognize that less than +% the entire sample was used to compute the 0-lag term +% FILTEREDPRICE - Prices used in the RK +% FILTEREDTIME - Time stamps of filtered prices used in the RK +% NOISEVARIANCE - Bandi-Russell noise variance estimate. Empty if not needed to +% compute the optimal bandwidth or number of points to jitter +% DEBIASEDNOISEVARIANCE - Bias adjusted estimate of the noise variance +% JITTERLAGS - Present only if the end points are jittered, contains the +% number of points that used to implement the pre-averaging. +% +% COMMENTS: +% For best results: +% - Use prices sampled at close to their highest frequency. This improves the estimate of noise. +% - Use business time sampling with at most a small number of trades between samples (preferably +% 1, but usually <15) +% - If using calendar time sampling, sample close to the limit of the data availability (e.g. 5-15 +% seconds for a stock that trades a few thousand times per day) +% - When sampling less frequently (e.g. 5 - 30 minutes) the standard realized variance is +% probably more appropriate +% +% This function is essentially a wrapper around six other functions. If interested in performance, functions +% not used (especially realized_kernel_parameter_check) can be omitted +% 1. realized_kernel_parameter_check - Input validation. +% 2. realized_noise_estimate - Estimate the noise variance and a lower bound for IQ for use in +% selecting the bandwidth or number of lags to use when jittering end points. +% 3. realized_kernel_bandwidth - Compute the optimal bandwidth using the outputs of +% realized_noise_variance +% 4. realized_kernel_jitter_lag_length - Compute the optimal number of points to jitter +% 5. realized_price_filter - Filter the original prices to compute the returns used for +% computing realized autocovariances +% 6. realized_kernel_weights computes the weights for a kernel and bandwidth +% 7. realized_kernel_core computes the estimate using the weights and returns. +% +% EXAMPLES: +% % Default usage with 'nonflatparzen', 'BusinessTime' sampling with interval 1 +% RK = realized_kernel(PRICE) +% +% % 10-tick realized kernel with 'nonflatparzen' +% RK = realized_kernel(PRICE,TIME,'wall','BusinessTime',10) +% +% % Realized Kernel using a Cubic kernel with other options at their default +% options = realized_options('Kernel'); +% options.kernel = 'cubic'; +% RK = realized_kernel(PRICE,TIME,'wall','BusinessTime',1,options) +% +% See also REALIZED_OPTIONS, REALIZED_NOISE_ESTIMATE, REALIZED_VARIANCE, +% REALIZED_VARIANCE_OPTIMAL_SAMPLING, REALIZED_RANGE, REALIZED_QUANTILE_VARIANCE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 1 + m = length(price); + time = linspace(9.5*3600,16*3600,m)'; + timeType = 'seconds'; + samplingType = 'businesstime'; + samplingInterval = 1; + options = realized_options('kernel'); + case 5 + options = realized_options('kernel'); + case 6 + % Nothing + otherwise + error('One, five or six inputs required.') +end + +[errorMessage, options] = realized_kernel_parameter_check(price,time,timeType,samplingType,samplingInterval,options); + +if ~isempty(errorMessage ) + error(errorMessage) +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +isJittered = strcmpi(options.endTreatment,'jitter'); + +% Inserted to protect against inputing integer times +time = double(time); + +% 2. [Optional] If options.bandWidth is not provided, estimate the Noise Variance. Also needed to estimate the number +% of lags or the amount of jitter +if isempty(options.bandwidth) || (isJittered && isempty(options.jitterLags)) + [noiseVariance, debiasedNoiseVariance, IQEstimate] = realized_noise_estimate(price, time, timeType, options); + diagnostics.noiseVariance=noiseVariance; + diagnostics.debiasedNoiseVariance=debiasedNoiseVariance; + % Select the correct noise variance estimate + if options.useDebiasedNoise + selectedNoiseVariance = debiasedNoiseVariance; + else + selectedNoiseVariance = noiseVariance; + end +end + + +% 3. Compute bandwidth is needed +if isempty(options.bandwidth) + % Compute the bandwidth + options.bandwidth = realized_kernel_bandwidth(selectedNoiseVariance, IQEstimate, options); + % Check that the bandwidth is not too large +end + +% 4. If jittering is required, perform the optimal jittering prior to filtering prices. +if isJittered + if isempty(options.jitterLags) + jitterLags = realized_kernel_jitter_lag_length(selectedNoiseVariance, IQEstimate, options.kernel, options.filteredN); + options.jitterLags = jitterLags; + end + % Jitter the price + m = length(price); + jl = options.jitterLags; + p0 = mean(price(1:jl)); + p1 = mean(price(m-jl+1:m)); + t0 = time(ceil(mean(1:jl))); + t1 = time(floor(mean(m-jl+1:m))); + price = [p0;price(jl+1:m-jl);p1]; + time = [t0;time(jl+1:m-jl);t1]; +end + +% 5. Filter the price +[filteredPrice,filteredTime] = realized_price_filter(price,time,timeType,samplingType,samplingInterval); +returns = diff(log(filteredPrice)); + +% 6. Compute the weights +weights=realized_kernel_weights(options); + +% 7. Compute the realized kernel +rk = realized_kernel_core(returns, weights, options); + + +% Clean up +n=size(filteredPrice,1); +m=size(price,1); + +% Construct the diagnostics vector +diagnostics.kernel=options.kernel; +diagnostics.bandwidth=options.bandwidth; +diagnostics.filteredPrice=filteredPrice; +diagnostics.filteredTime=filteredTime; +diagnostics.weights = weights; +if isJittered + diagnostics.jitterLags = options.jitterLags; +end + +% Compute the debiasing adjustment +if isJittered + diagnostics.adjustment = 1; + % FIXME: Should be a debiasing adjustment here +else + diagnostics.adjustment = (filteredTime(n-round(options.bandwidth))-filteredTime(1+round(options.bandwidth)))/(time(m)-time(1)); +end + +% Compute the bias adjusted RK +rkAdjusted = rk / diagnostics.adjustment; + + + + + + + + + + + + + + + + + +function [errorMessage, options] = realized_kernel_parameter_check(price,time,timeType,samplingType,samplingInterval,options) +% Support function for realized_kernel that does input validation +% +% USAGE: +% [ERRORMESSAGE,OPTIONS] = realized_kernel_parameter_check(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINVERVAL,OPTIONS) +% +% INPUTS: +% See realized_kernel +% +% OUTPUT: +% ERRORMESSAGE - String containing a description of the error if one is detected. Empty if no +% error. +% OPTIONS - A realized_kernel options structure with the additional field +% filteredN - Number of observations that are used to compute the kernel. This is +% needed for computing the optimal bandwidth. +% +% COMMENTS: +% See realized_options for a description of the other fields in OPTIONS +% +% See also REALIZED_KERNEL, REALIZED_OPTIONS + + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + + +% initialized errorMessage +errorMessage = []; + +% Price +if size(price,2)>size(price,1) + price=price'; +end +if size(price,2)>1 + errorMessage = 'PRICE must be a m by 1 vector.'; + return +end + +% Time +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + errorMessage = 'TIME must be sorted and increasing'; + return +end +if size(time,2)>1 || length(time)~=length(price) + errorMessage = 'TIME must be a m by 1 vector the same size as PRICE.'; + return +end +% TimeType +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','unit'}) + errorMessage = 'TIMETYPE must be one of ''wall'', ''seconds'' or ''unit''.'; + return +end +% Sampling Type +samplingType=lower(samplingType); +if ~ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + errorMessage = 'SAMPLINGTYPE must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.'; + return +end + +m=size(price,1); +t0=time(1); +tT=time(m); +if ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform'}) + % Must be a scalar integer + if ~isscalar(samplingInterval) || floor(samplingInterval)~=samplingInterval || samplingInterval<1 + errorMessage = 'SAMPLINGINTERVAL must be a positive integer for the SAMPLINGTYPE selected.'; + return + end +else + if size(samplingInterval,2)>size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + if ~(any(samplingInterval>=t0) && any(samplingInterval<=tT)) + errorMessage = 'At least one sampling interval must be between min(TIME) and max(TIME) when using ''Fixed'' as SAMPLINGTYPE.'; + return + end + if any(diff(samplingInterval)<=0) + errorMessage = 'When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.'; + return + end +end + + +% Options + + +% List of flat top kernels +flatTopKernelList = {'bartlett','twoscale','2ndorder','epanechnikov',... + 'cubic','multiscale','5thorder','6thorder','7thorder','8thorder','parzen',... + 'th1','th2','th5','th16'}; + +% List of non flat top kernels +nonFlatTopKernelList = {'nonflatparzen','qs','fejer','thinf','bnhls'}; + +% Combined kernel list +kernelList = [flatTopKernelList nonFlatTopKernelList]; + +% Check fields for valid values +optionsFieldNames = fieldnames(options); +% Insert any missing fiedls +defaultOptions = realized_options('Kernel'); +defaultFieldNames = fieldnames(defaultOptions); +missingFields = setdiff(defaultFieldNames,optionsFieldNames); +if ~isempty(missingFields) + for i = 1:length(missingFields) + options.(missingFields{i}) = defaultOptions.(missingFields{i}); + end +end + +for i=1:length(optionsFieldNames) + fieldName = optionsFieldNames{i}; + fieldValue = options.(fieldName); + if ischar(fieldValue) + fieldValue = lower(fieldValue); + options.(fieldName) = fieldValue; + end + + switch fieldName + case {'kernel','medFrequencyKernel'} + % Member of kernelList + if ~ismember(fieldValue,kernelList) + errorMessage = ['OPTIONS.' fieldName ' must be one of the listed types.']; + return + end + case {'bandwidth','medFrequencyBandwidth'} + % Non-negative scalar + if ~isempty(fieldValue) && ~isnonnegativescalar(fieldValue) + errorMessage = ['OPTIONS.' fieldName ' must a non-negative scalar.']; + return + end + case 'endTreatment' + % String + if ~ismember(fieldValue,{'jitter','stagger'}) + errorMessage = 'OPTIONS.endTreatment must be either ''Jitter'' or ''Stagger''.'; + return + end + case {'jitterLags','maxBandwidth'} + % Non-negative scalar integer + if ~isempty(fieldValue) && ~isnonnegativescalarinteger(fieldValue) + errorMessage = ['OPTIONS.' fieldName ' must be a non-negative scalar integer.']; + return + end + case {'useDebiasedNoise','useAdjustedNoiseCount'} + % Logical or scalar + if ~islogical(fieldValue) && ~ismember(fieldValue,[0 1]) + errorMessage = 'OPTIONS.useDebiasedNoise must be a logical value.'; + return + end + case 'maxBandwidthPerc' + % Scalar 0<=fieldvalue<=1 + if ~isempty(fieldValue) && ~isnonnegativescalar(fieldValue) && fieldValue>1 + errorMessage = 'OPTIONS.maxBandwidthPerc must be a non-negative scalar between 0 and 1.'; + return + end + case {'IQEstimationSamplingType','medFrequencySamplingType','noiseVarianceSamplingType'} + % One of the sampling types + if ~ismember(fieldValue,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + errorMessage = ['OPTIONS.' fieldName ' must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.']; + return + end + case {'medFrequencySamplingInterval','noiseVarianceSamplingInterval','IQEstimationSamplingInterval'} + % Non-negative scalar, less that 1 if timeType is unit + if isempty(fieldValue) || ~isnonnegativescalar(fieldValue) + errorMessage = ['OPTIONS.' fieldName ' must be a non-negative scalar between 0 and 1.']; + return + end + if strcmp(timeType,'unit') && fieldValue>1 + errorMessage = ['OPTIONS.' fieldName ' must be less than 1 if TIMETYPE when ''unit''.']; + return + end + end +end + +% Compute the number of prices available in the filtered series +if ~strcmpi(samplingType,'businesstime') || samplingInterval~=1 + tempFilteredPrice = realized_price_filter(price,time,timeType,samplingType,samplingInterval); + options.filteredN = length(tempFilteredPrice); +else + options.filteredN = length(price); +end + + +function condition = isnonnegativescalarinteger(x) +% Function that returns logical true if that input is a non-empty, scalar integer >=0 +condition = ~isempty(x) && isscalar(x) && x>=0 && x==floor(x); + + +function condition = isnonnegativescalar(x) +% Function that returns logical true if that input is a non-empty scalar >=0 +condition = ~isempty(x) && isscalar(x) && x>=0; \ No newline at end of file diff --git a/realized/realized_kernel_bandwidth.m b/realized/realized_kernel_bandwidth.m new file mode 100644 index 0000000..abb7a25 --- /dev/null +++ b/realized/realized_kernel_bandwidth.m @@ -0,0 +1,126 @@ +function bandwidth = realized_kernel_bandwidth(noiseVariance, IQEstimate, options) +% Estimation of the optimal bandwidth for use in Realized Kernels +% +% USAGE: +% [BANDWIDTH] = realized_kernel_select_bandwidth(NOISEVARIANCE,IQESTIMATE,OPTIONS) +% +% INPUTS: +% NOISEVARIANCE - Estimate of noise variance +% IQESTIMATE - Estimate of integrated quarticity +% OPTIONS - Realized kernel options structure. See help realized_options +% +% OUTPUTS: +% BANDWIDTH - Optimal bandwidth computed using plug-in estimates of unknown quantities +% +% COMMENTS: +% This is a helper function for REALIZED_KERNEL. See Barndorf-Nielsen, Hansen, Lunde and Shephard +% (2008) for details about the optimal selection of bandwidth +% +% See also REALIZED_KERNEL, REALIZED_NOISE_ESTIMATE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=3 + error('Three inputs required.') +end + +% List of flat top kernels +flatTopKernelList = {'bartlett','twoscale','2ndorder','epanechnikov',... + 'cubic','multiscale','5thorder','6thorder','7thorder','8thorder','parzen',... + 'th1','th2','th5','th16'}; + +% List of non flat top kernels +nonFlatTopKernelList = {'nonflatparzen','qs','fejer','thinf','bnhls'}; + +% Combined kernel list +kernelList = [flatTopKernelList nonFlatTopKernelList]; + +if ~isfield(options,'kernel') || ~ismember(options.kernel,kernelList) + error('KERNEL must be a field of OPTIONS and one of the listed types.') +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Retrieve Kernel Specific information +switch lower(options.kernel) + case {'bartlett','twoscale'} + cStar = 2.28; + kernelType = 2; + case '2ndorder' + cStar = 3.42; + kernelType = 2; + case 'epanechnikov' + cStar = 2.46; + kernelType = 2; + case {'cubic','multiscale'} + cStar = 3.68; + kernelType = 1; + case '5thorder' + cStar = 3.70; + kernelType = 1; + case '6thorder' + cStar = 3.97; + kernelType = 1; + case '7thorder' + cStar = 4.11; + kernelType = 1; + case '8thorder' + cStar = 4.31; + kernelType = 1; + case 'parzen' + cStar = 4.77; + kernelType = 1; + case 'th1' + cStar = 3.70; + kernelType = 1; + case 'th2' + cStar = 5.74; + kernelType = 1; + case 'th5' + cStar = 8.07; + kernelType = 1; + case 'th16' + cStar = 39.16; + kernelType = 1; + case 'nonflatparzen' + cStar = ((12)^2/0.269)^(1/5); + kernelType = 3; + case 'qs' + cStar = ((1/5)^2/(3*pi/5))^(1/5); + kernelType = 3; + case 'fejer' + cStar = ((2/3)^2/(pi/3))^(1/5); + kernelType = 3; + case 'thinf' + cStar = ((pi^2/2)^2/(.52))^(1/5); + kernelType = 3; + case 'bnhls' + cStar = (1^2/(5/4))^(1/5); + kernelType = 3; + otherwise + error('KERNEL must be one of the listed types.') +end + + +% Compute the bandwidth +xiSquared = noiseVariance/sqrt(IQEstimate); +if xiSquared>1 + warning('oxfordRealized:excessiveLags','IQ estimaed o be close to 0. Please check results'); + xiSquared = 1; +end +% Get the size of the filtered data +nMax = options.filteredN; + +if kernelType == 1 + bandwidth = cStar * (xiSquared)^(1/2) * nMax^(1/2); +elseif kernelType ==2 + bandwidth = cStar * (xiSquared)^(2/3) * nMax^(2/3); +elseif kernelType ==3 + bandwidth = cStar * (xiSquared)^(2/5) * nMax^(3/5); +end diff --git a/realized/realized_kernel_core.m b/realized/realized_kernel_core.m new file mode 100644 index 0000000..bb5091e --- /dev/null +++ b/realized/realized_kernel_core.m @@ -0,0 +1,115 @@ +function rk = realized_kernel_core(returns, weights, options) +% Realized Kernel core routine that computes the value of a realized kernel +% given a set of returns and weights. +% +% USAGE: +% [RK] = realized_kernel_core(RETURNS,WEIGHTS,OPTIONS) +% +% INPUTS: +% RETURNS - m by 1 column vector of returns +% WEIGHTS - H by 1 column vector of kernel weights corresponding to lags 1, 2, ..., H. H should +% be much smaller than m +% OPTIONS - A realized kernel options structure. See help realized_options for details +% +% OUTPUTS: +% RK - Realized kernel value +% +% COMMENTS: +% This is a helper function for REALIZED_KERNEL +% +% See also REALIZED_KERNEL, REALIZED_OPTIONS, REALIZED_KERNEL_WEIGHTS, REALIZED_KERNEL_BANDWIDTH + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=3 + error('Three inputs required.') +end +if size(returns,2)>size(returns,1) + returns=returns'; +end +if size(returns,2)>1 + error('RETURNS must be a m by 1 vector.') +end +if size(weights,2)>size(weights,1) + weights=weights'; +end +if size(weights,2)>1 + error('WEIGHTS must be a H by 1 vector.') +end + +% Get the number of returns +m=size(returns,1); +if length(weights)>=m + warning('oxfordRealized:realizedKernelLength','The length of WEIGHTS is longer than the length of RETURNS.\n The weights are being truncated at N-1 where N is the number of returns') + weights = weights(1:m-1); +elseif (isfield(options,'maxBandwidthPerc') && ~isempty(options.maxBandwidthPerc)) || (isfield(options,'maxBandwidth') && ~isempty(options.maxBandwidth)) + warningString = []; + + if ~isempty(options.maxBandwidthPerc) && (length(weights)>(options.maxBandwidthPerc * options.filteredN)) + options.maxBandwidth = round(options.maxBandwidthPerc * options.filteredN); + warningString = ['The estimated bandwidth requires a lag length larger than ' ... + num2str(100*options.maxBandwidthPerc) ' %% of the available data. Bandwidth has ' ... + 'been truncated to ' num2str(options.maxBandwidth) '.']; + elseif ~isempty(options.maxBandwidth) && length(weights)>options.maxBandwidth + warningString = ['The estimated bandwidth requires a lag length larger than ' ... + num2str(options.maxBandwidth) '. Bandwidth has ' ... + 'been truncated to ' num2str(options.maxBandwidth) '.']; + end + + if ~isempty(warningString) + warning('oxfordRealized:realizedKernelLength',warningString); + weights = weights(1:options.maxBandwidth); + end +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Extract relevant fields form OPTIONS +isJittered = strcmpi(options.endTreatment,'jitter'); +% Get the size of the kernel +H=length(weights); +if isJittered + % Use all returns when computing autocovariances + gammaMinus = zeros(H,1); + gammaPlus = zeros(H,1); + % Loop and compute the values for gamma + for i=1:H + returnsMinus = returns(1:m-i); + returnsPlus = returns(i+1:m); + gammaMinus(i) = returnsMinus' * returnsPlus; + gammaPlus(i) = returnsMinus' * returnsPlus; + end + % Compute the 0-lag gamma using all returns + gamma0 = returns' * returns; +else + % When not jittered a different strategy is used + + % Construct the "central" set of returns + returnsBase = returns(H+1:m-H); + % Initialized placeholders for the terms of gamma + gammaMinus = zeros(H,1); + gammaPlus = zeros(H,1); + % Loop and compute the values for gamma + for i=1:H + returnsMinus = returns(H+1-i:m-H-i); + returnsPlus = returns(H+1+i:m-H+i); + gammaMinus(i) = returnsMinus' * returnsBase; + gammaPlus(i) = returnsBase' * returnsPlus; + end + % Compute the 0-lag gamma + gamma0 = returnsBase' * returnsBase; +end + +% Construct the kernel +if ~isempty(weights) + rk = gamma0 + weights'*(gammaMinus+gammaPlus); +else + warning('oxfordRealized:realizedKernelLength','The number of lags used was 0.'); + rk = gamma0; +end \ No newline at end of file diff --git a/realized/realized_kernel_jitter_lag_length.m b/realized/realized_kernel_jitter_lag_length.m new file mode 100644 index 0000000..01e9541 --- /dev/null +++ b/realized/realized_kernel_jitter_lag_length.m @@ -0,0 +1,202 @@ +function jitterLags = realized_kernel_jitter_lag_length(noiseEstimate,iqEstimate,kernel,N) +% Computes the optimal amount of end point jitter given a kernel, noise estimate, integrated +% quarticity estimate and number of observations. +% +% USAGE: +% [JITTERLAGS] = realized_kernel_weights(NOISEESTIMATE,IQESTIMATE,KERNEL,N) +% +% INPUTS: +% NOISEESTIMATE - Estimated variance of the noise present in a high freuqency asset price (see +% realized_kernel_select_lag_length) +% IQESTIMATE - Estimated integrated quarticity. For the purposes of estimating the number of +% points to jitter it is often reasonable to use the square of a low frequence +% IV measure. +% KERNEL - String containing one of the supported kernel types: +% Non-flat-top, weakly positive, n^(1/5) rate: +% - 'nonflatparzen' [RECOMMENDED] Parzen kernel applied to non-flat-top case +% - 'qs' Quadratic Spectral +% - 'fejer' Fejer kernel +% - 'thinf' Tukey-Hanning kernel with infinite lag order +% - 'bnhls' Kernel proposed by Barndorf-Neilsen, Hansen, Lunde and Shephard +% Flat-top, n^(1/4) rate: +% - 'parzen' Parzen's kernel +% - 'th1' Tukey Hanning kernel with power 1 +% - 'th2' Tukey Hanning kernel with power 2 +% - 'th5' Tukey Hanning kernel with power 5 +% - 'th16' Tukey Hanning kernel with power 16 +% - 'cubic','multiscale' 3rd order (cubic) kernel, which +% is asymptotically equivalent to the multiscale estimator +% - '5thorder' 5th order Kernel +% - '6thorder' 6th order Kernel +% - '7thorder' 7th order Kernel +% - '8thorder' 8th order Kernel +% Flat-top, n^(1/6) rate: +% - 'bartlett','twoscale' Bartlett kernel, which is +% asymptotically equivalent to the two-scale estimator +% - '2ndorder' 2nd order (quadratic) kernel +% - 'epanechnikov' Epanechnikov kernel +% N - Number of observation of the price +% +% OUTPUTS: +% JITTERLAGS - Estimated optimal number of lags to jitter the end points of a kernel. If 1 +% then no pre-averaging is needindicated +% +% COMMENTS: +% This is a helper function for REALIZED_KERNEL. See Barndorf-Nielsen, +% Hansen, Lunde and Shephard (2008a, 2008b) for details about the kernel and +% their properties. +% +% See also REALIZED_KERNEL_SELECT_LAG_LENGTH, REALIZED_VARIANCE, REALIZED_KERNEL, +% REALIZED_PRICE_FILTER, REALIZED_KERNEL_WEIGHTS + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=4 + error('Four inputs required.') +end +if length(noiseEstimate)>1 || noiseEstimate<0 + error('NOISEESTIMATE must be a non-negative scalar.'); +end +if length(iqEstimate)>1 || iqEstimate<0 + error('IQESTIMATE must be a non-negative scalar.'); +end +if ~ismember(kernel,{'bartlett','twoscale','2ndorder','epanechnikov','cubic','multiscale','5thorder','6thorder','7thorder','8thorder','parzen','th1','th2','th5','th16','nonflatparzen','qs','fejer','thinf','bnhls'}) + error('KERNEL must be one of the listed types.') +end + +if ~isscalar(N) || N<1 || floor(N)~=N + error('N must be an integer greater than 1.') +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Look up table +switch lower(kernel) + case {'bartlett','twoscale'} + cStar = 2.28; + k00 = 1/3; + kernelType = 2; + case '2ndorder' + cStar = 3.42; + k00 = 1/5; + kernelType = 2; + case 'epanechnikov' + cStar = 2.46; + k00 = 8/15; + kernelType = 2; + case {'cubic','multiscale'} + cStar = 3.68; + k00 = 0.371; + k11 = 1.20; + k22 = 12.0; + kernelType = 1; + case '5thorder' + k00 = 0.391; + k11 = 1.42; + k22 = 17.1; + cStar = 3.70; + kernelType = 1; + case '6thorder' + k00 = 0.471; + k11 = 1.55; + k22 = 22.8; + cStar = 3.97; + kernelType = 1; + case '7thorder' + k00 = 0.533; + k11 = 1.71; + k22 = 31.8; + cStar = 4.11; + kernelType = 1; + case '8thorder' + k00 = 0.582; + k11 = 1.87; + k22 = 43.8; + cStar = 4.31; + kernelType = 1; + case 'parzen' + k00 = 0.269; + k11 = 1.50; + k22 = 24.0; + cStar = 4.77; + kernelType = 1; + case 'th1' + k00 = 0.375; + k11 = 1.23; + k22 = 12.1; + cStar = 3.70; + kernelType = 1; + case 'th2' + k00 = 0.219; + k11 = 1.71; + k22 = 41.7; + cStar = 5.74; + kernelType = 1; + case 'th5' + k00 = 0.097; + k11 = 3.50; + k22 = 489.0; + cStar = 8.07; + kernelType = 1; + case 'th16' + k00 = 0.032; + k11 = 10.26; + k22 = 14374.0; + cStar = 39.16; + kernelType = 1; + case 'nonflatparzen' + cStar = ((12)^2/0.269)^(1/5); + k00 = .269; + kernelType = 3; + case 'qs' + cStar = ((1/5)^2/(3*pi/5))^(1/5); + k00 = 3*pi/5; + kernelType = 3; + case 'fejer' + cStar = ((2/3)^2/(pi/3))^(1/5); + k00 = pi/3; + kernelType = 3; + case 'thinf' + cStar = ((pi^2/2)^2/(.52))^(1/5); + k00 = 0.52; + kernelType = 3; + case 'bnhls' + cStar = (1^2/(5/4))^(1/5); + k00 = 5/4; + kernelType = 3; + otherwise + error('KERNEL must be one of the listed types.') +end + + +% Compute the quantities necessary +if kernelType ==1 + % n^1/4 flat top + % Approximate at the constant variance solution + d=k00*k22/k11^2; + fd = sqrt(1+sqrt(1+3*d)); + g = sqrt(k00*k11)*(1/fd + fd); + avar = 16/3 * g * noiseEstimate * iqEstimate^(3/4); + power = 1/4; +elseif kernelType == 2 + % n^1/6 flat top + avar = 6 * cStar * k00 * noiseEstimate^(4/3) * iqEstimate^(2/3); + power = 1/6; +elseif kernelType == 3 + % n^1/5 non flat top + avar = 5 * cStar * k00 * noiseEstimate^(4/5) * iqEstimate^(4/5); + power = 1/5; +end + +% Problem is to min 8*noise^2*jitterLag^(-2) + avar * (N-jitterLag)^(-2*power) +% jittering over m data points, N observations in total +MSE = inf*ones(N-1,1); +for m=1:(N-1) + MSE(m) = 8 * noiseEstimate^2 * m^(-2) + avar * (N-m)^(-2*power); +end + +% Find the minimum, which may be 1 +[temp,jitterLags] = min(MSE); \ No newline at end of file diff --git a/realized/realized_kernel_weights.m b/realized/realized_kernel_weights.m new file mode 100644 index 0000000..be41fb8 --- /dev/null +++ b/realized/realized_kernel_weights.m @@ -0,0 +1,124 @@ +function weights=realized_kernel_weights(options) +% Computes weights for Realized Kernels +% +% USAGE: +% [WEIGHTS] = realized_kernel_weights(OPTIONS) +% +% INPUTS: +% OPTIONS - A realized kernel options structure. See help realized_options for details +% +% OUTPUTS: +% WEIGHTS - H by 1 vector of kernel weights where H depends on the bandwidth and kernel +% +% COMMENTS: +% This is a helper function for REALIZED_KERNEL. See Barndorf-Nielsen, +% Hansen, Lunde and Shephard (2008a, 2008b) for details about realized kernels and +% their properties. +% +% See also REALIZED_KERNEL, REALIZED_KERNEL_BANDWIDTH, + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=1 + error('One input required.') +end + +% List of flat top kernels +flatTopKernelList = {'bartlett','twoscale','2ndorder','epanechnikov',... + 'cubic','multiscale','5thorder','6thorder','7thorder','8thorder','parzen',... + 'th1','th2','th5','th16'}; + +% List of non flat top kernels +nonFlatTopKernelList = {'nonflatparzen','qs','fejer','thinf','bnhls'}; + +% Combined kernel list +kernelList = [flatTopKernelList nonFlatTopKernelList]; + +if ~isfield(options,'kernel') || ~ismember(options.kernel,kernelList) + error('KERNEL must be a field of OPTIONS and one of the listed types.') +end + +if ~isfield(options,'bandwidth') || options.bandwidth<0 + error('BANDWIDTH must be a field of OPTIONS and a non-negative scalar.') +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Take relevant fields +kernel = options.kernel; +bandwidth = options.bandwidth; + +% A big lookup table +if bandwidth>0 + if ismember(options.kernel,flatTopKernelList) + % If it is flat top then the first lag is actually 0 which produces a weights of 1 + H = round(bandwidth); + x = (1:H)'; + x = (x-1)/H; + else + H = bandwidth; + end + + switch lower(kernel) + case {'bartlett','twoscale'} + weights = 1-x; + case {'2ndorder'} + weights = 1-2*x+x.^2; + case {'epanechnikov'} + weights = 1-x.^2; + case {'cubic','multiscale'} + weights = 1-2*x.^2+2*x.^3; + case '5thorder' + weights = 1-10*x.^3+15*x.^4-6*x.^5; + case '6thorder' + weights = 1-15*x.^4+24*x.^5-10*x.^6; + case '7thorder' + weights = 1-21*x.^5+35*x.^6-15*x.^7; + case '8thorder' + weights = 1-28*x.^6+48*x.^7-21*x.^8; + case 'parzen' + weights = (1-6*x.^2+6*x.^3).*(x>=0 & x<=1/2) + 2*(1-x).^3.*(x>1/2 & x<1); + case 'th1' + weights = sin(pi/2*(1-x)).^2; + case 'th2' + weights = sin(pi/2*(1-x).^2).^2; + case 'th5' + weights = sin(pi/2*(1-x).^5).^2; + case 'th16' + weights = sin(pi/2*(1-x).^16).^2; + case 'nonflatparzen' + x = (1:H)'; + x = x./(H+1); + weights = (1-6*x.^2+6*x.^3).*(x>=0 & x<=1/2) + 2*(1-x).^3.*(x>1/2 & x<1); + case 'qs' + % Truncate at 30 * H where H is BW + x = unique(round(1:30*H))'; + x = x./(H+1); + weights = 3./x.^2 .* (sin(x)./x - cos(x)); + case 'fejer' + % Truncate at 30 * H where H is BW + x = unique(round(1:30*H))'; + x = x./(H+1); + weights = (sin(x)./x).^2; + case 'thinf' + % Truncate at 4 * H where H is BW + x = unique(round(1:4*H))'; + x = x./(H+1); + weights = sin((pi/2).*exp(-x)).^2; + case 'bnhls' + % Truncate at 10 * H where H is BW + x = unique(round(1:10*H))'; + x = x./(H+1); + weights = (1+x).*exp(-x); + otherwise + error('OPTIONS.KERNEL must be one of the listed types.') + end +else + weights=[]; +end \ No newline at end of file diff --git a/realized/realized_min_med_variance.m b/realized/realized_min_med_variance.m new file mode 100644 index 0000000..a7d3770 --- /dev/null +++ b/realized/realized_min_med_variance.m @@ -0,0 +1,191 @@ +function [medRV,minRV,medRVSS,minRVSS]=realized_min_med_variance(price,time,timeType,samplingType,samplingInterval,subsamples) +% Estimates truncated realized variance using the median and minimum method of Andersen, Dobrev and Schaumburg +% +% USAGE: +% [MEDRV,MINRV] = realized_medrv(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL,SAMPLESPERBIN) +% [MEDRV,MINRV,MEDRVSS,MINRVSS] = realized_medrv(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL,SAMPLESPERBIN,SUBSAMPLES) +% +% INPUTS: +% PRICE - m by 1 vector of high frequency prices +% TIME - m by 1 vector of times where TIME(i) corresponds to PRICE(i) +% TIMETYPE - String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight on the first day. +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the other types and can be +% applied to data from more than one calendar day +% SAMPLINGTYPE - String describing the type of sampling to use when +% filtering PRICE +% 'CalendarTime' - Sample in calendar time using observations separated by +% SAMPLINGINTERVAL seconds +% 'CalendarUniform' - Sample in calendar time using SAMPLINGINTERVAL +% observations spread uniformly between TIME(1) and TIME(m) +% 'BusinessTime' - Sample in business (tick) time using observation separated +% by SAMPLINGINTERVAL ticks +% 'BusinessUniform' - Sample in business (tick) time using observations +% uniformly spaced in business time. +% 'Fixed' - Sample at specific points in time. When using fixed, +% SAMPLINGINTERVAL must be a n by 1 vector of times with the same TIMETYPE +% as TIME (i.e. seconds if TIME is in seconds) +% SAMPLINGINTERVAL - Scalar integer or n by 1 vector whose meaning depends on SAMPLINGTYPE +% SUBSAMPLES - [OPTIONAL] Scalar integer indicating the number of subsample realized +% variance estimators to average with the original realized variance. +% Subsample realized variances are based on prices uniformly spaced between +% the times (Calendar sampling) or ticks (Business sampling). SUBSAMPLES should +% be greater than 1, since 1 uses a single subsample and so is equivalent +% to the original RV will compute a subsample realized variance using the +% mid-point of the price sample points, 2 will use the original sample and +% the midpoint between the original sampling times, and so on. +% In general this number should be small so the subsample estimators will be "sparse". +% +% OUTPUTS: +% MEDRV - Median RV estimate +% MINRV - Minimum RV estimate +% MEDRVSS - Subsampled version of median RV estimate +% MINRVSS - Subsampled version of minimum RV estimate +% +% COMMENTS: +% +% EXAMPLE: +% % Using all 1-minute returns between 9:30:00 and 16:00:00 +% fixedInterval = seconds2wall(wall2seconds(93000):60:wall2seconds(160000)); +% [MEDRV,MINRV] = realized_medrv(PRICE,TIME,'wall','Fixed',fixedInterval) +% +% % Using all 5-minute returns between 9:30:00 and 16:00:00, but subsampling every minute +% fixedInterval = seconds2wall(wall2seconds(93000):300:wall2seconds(160000)); +% [MEDRV,MINRV,MEDRVSS,MINRVSS] = realized_medrv(PRICE,TIME,'wall','Fixed',fixedInterval,5) +% +% See also REALIZED_BIPOWER_VARIATION, REALIZED_KERNEL, REALIZED_QUANTILE_VARIANCE, +% REALIZED_RANGE, REALIZED_PRICE_FILTER + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 10/24/2011 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin<5 || nargin>6 + error('Five or Six inputs required.') +end +if size(price,2)>size(price,1) + price=price'; +end +if size(price,2)>1 + error('PRICE must be a m by 1 vector.') +end +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + error('TIME must be sorted and increasing') +end +if size(time,2)>1 || length(time)~=length(price) + error('TIME must be a m by 1 vector.') +end +% Inserted to protect against inputing integer times +time = double(time); + +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','unit'}) + error('TIMETYPE must be one of ''wall'', ''seconds'' or ''unit''.'); +end +samplingType=lower(samplingType); +if ~ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + error('SAMPLINGTYPE must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.'); +end + +m=size(price,1); +t0=time(1); +tT=time(m); +if ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform'}) + % Must be a scalar integer if timeType is seconds or wall + if ismember(timeType,{'wall','seconds'}) + if ~isscalar(samplingInterval) || floor(samplingInterval)~=samplingInterval || samplingInterval<1 + error('SAMPLINGINTERVAL must be a positive integer for the SAMPLINGTYPE selected when using ''wall'' or ''seconds'' as TIMETYPE.') + end + else + if ~isscalar(samplingInterval) || samplingInterval<0 + error('SAMPLINGINTERVAL must be a positive value for the SAMPLINGTYPE selected when using ''unit'' as TIMETYPE.') + end + end +else + if size(samplingInterval,2)>size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + if ~(any(samplingInterval>=t0) && any(samplingInterval<=tT)) + error('At least one sampling interval must be between min(TIME) and max(TIME) when using ''Fixed'' as SAMPLINGTYPE.') + end + if any(diff(samplingInterval)<=0) + error('When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.') + end +end + +if nargin<6 || isempty(subsamples) + subsamples = 1; +end + +if nargin==6 && ~isempty(subsamples) + if ~isscalar(subsamples) || subsamples<0 || floor(subsamples)~=subsamples + error('SUBSAMPLES must be a non-negative scalar.') + end +end + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +logPrice = log(price); +% Convert times to unit if not already unit +if ~strcmp(timeType,'unit') + [time,~,~,samplingInterval]=realized_convert2unit(time,timeType,samplingType,samplingInterval); +end +% Since everything is converted to unit, set timeType to unit +timeType='unit'; +% m is the length of price + +% Filter prices and compute the RV +filteredLogPrice = realized_price_filter(logPrice,time,timeType,samplingType,samplingInterval); +% Construct the aggregated return series. Remember will need to skip +returns = diff(filteredLogPrice); +m = length(returns); + +returns2 = (sqrt(m)*returns).^2; +r2 = [returns2(1:m-2) returns2(2:m-1) returns2(3:m)]; +medRV = mean(median(r2,2)); +medRVScale = pi/(6-4*sqrt(3)+pi); +medRV = medRV*medRVScale ; + +r2 = [returns2(1:m-1) returns2(2:m)]; +minRV = mean(min(r2,[],2)); +minRVscale = pi/(pi-2); +minRV = minRV*minRVscale; + + + +subsampledLogPrices = realized_subsample(logPrice,time,timeType,samplingType,samplingInterval,subsamples); +medRVs = nan(m*subsamples,1); +minRVs = nan(m*subsamples,1); +medRVcount = 0; +minRVcount = 0; +for i=1:subsamples + filteredLogPrice = subsampledLogPrices{i}; + returns = diff(filteredLogPrice); + m = size(returns,1); + returns2 = m*returns.^2; + % MedRV + r2 = [returns2(1:m-2) returns2(2:m-1) returns2(3:m)]; + n = size(r2,1); + medRVs(medRVcount+(1:n)) = median(r2,2); + medRVcount = medRVcount + n; + % MinRV + r2 = [returns2(1:m-1) returns2(2:m)]; + n = size(r2,1); + minRVs(minRVcount+(1:n)) = min(r2,[],2); + minRVcount = minRVcount + n; +end +medRVSS = mean(medRVs(1:medRVcount)); +medRVSS = medRVSS * medRVScale; +minRVSS = mean(minRVs(1:minRVcount)); +minRVSS = minRVSS * minRVscale; \ No newline at end of file diff --git a/realized/realized_multiscale_variance.m b/realized/realized_multiscale_variance.m new file mode 100644 index 0000000..eb53426 --- /dev/null +++ b/realized/realized_multiscale_variance.m @@ -0,0 +1,374 @@ +function [rvms,rvmsSS,diagnostics] = realized_multiscale_variance(price,time,timeType,samplingType,samplingInterval,subsamples,options) +% Estimated quadratic variation using the Multi-Scale estimator of Zhang +% +% USAGE: +% RVMS = realized_multiscale_variance(PRICE) +% [RVMS,RVMSSS,DIAGNOSTICS] = realized_multiscale_variance(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL,SUBSAMPLES,OPTIONS) +% +% INPUTS: +% PRICE - m by 1 vector of high frequency prices +% TIME - [OPTIONAL] m by 1 vector of times where TIME(i) corresponds to PRICE(i). +% TIMETYPE - [OPTIONAL] String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS.mmm, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the other types and can be +% applied to data from more than one calendar day +% SAMPLINGTYPE - [OPTIONAL] String describing the type of sampling to use when +% filtering PRICE for estimating the fast scale estimator. +% 'CalendarTime' - Sample in calendar time using observations separated by +% SAMPLINGINTERVAL seconds +% 'CalendarUniform' - Sample in calendar time using SAMPLINGINTERVAL +% observations spread uniformly between TIME(1) and TIME(m) +% 'BusinessTime' - Sample in business (tick) time using observation separated +% by SAMPLINGINTERVAL ticks +% 'BusinessUniform' - Sample in business (tick) time using observations +% uniformly spaced in business time. +% 'Fixed' - Sample at specific points in time. When using fixed, +% SAMPLINGINTERVAL must be a n by 1 vector of times with the same TIMETYPE +% as TIME (i.e. seconds if TIME is in seconds) +% SAMPLINGINTERVAL - [OPTIONAL] Scalar integer or n by 1 vector whose meaning depends on the +% selected SAMPLINGTYPE +% OPTIONS - [OPTIONAL] Realized Two-Scale option structure initialized by calling +% realized_options('Multiscale'). See help realized_options for a description of +% available options. +% +% OUTPUTS: +% RVMS - Realized multi-scale variance estimate +% RVMSSS - Realized multi-scale variance estimate constructed by averaging RVMS across multiple +% initial observations. If SAMPLINGTYPE is 'BusinessTime' and SAMPLINGINTERAL is 1 +% then subsampling is not possible. +% DIAGNOSTICS - Structure of useful diagnostic information. Fields are +% BANDWIDTH - Ratio of slow scale to fast scale where the fast scale +% sampling is determined by SAMPLINGTYPE and SAMPLINGINTERVAL. +% NOISEVARIANCE - Bandi-Russell noise variance estimate. Empty if user +% supplies bandwidth. +% DEBIASEDNOISEVARIANCE - Bias adjusted estimate of the noise variance. +% IQESTIMATE - Estimate of IQ used. Empty if not needed. Empty if user +% supplies bandwidth. +% +% COMMENTS: +% For best results: +% - Use prices sampled close to the highest frequency available, if not using 'BusinessTime' and +% - If using calendar time sampling, sample close to the limit of the data availability (e.g. 5-15 +% seconds for a stock that trades a few thousand times per day) +% - When sampling less frequently (e.g. 5 - 30 minutes) standard realized variance is +% probably more appropriate +% +% EXAMPLE: +% % Default usage with 'BusinessTime' sampling with interval 1 and automatic bandwidth selection +% RVMS = realized_multiscale_variance(PRICE) +% +% % 5-tick multi-scale variance with automatic bandwidth selection +% RVMS = realized_multiscale_variance(PRICE,TIME,'wall','BusinessTime',5) +% +% % Two scale variance with a bandwidth of 30 sampling at every tick +% options = realized_options('Multiscale'); +% options.bandwidth = 30; +% RVMS = realized_multiscale_variance(PRICE,TIME,'wall','BusinessTime',1,0,options) +% +% % 5-tick multi-scale variance with automatic bandwidth selection and dense subsampling +% RVMS = realized_multiscale_variance(PRICE,TIME,'wall','BusinessTime',5,4) +% +% See also REALIZED_OPTIONS, REALIZED_NOISE_ESTIMATE, REALIZED_VARIANCE, +% REALIZED_VARIANCE_OPTIMAL_SAMPLING, REALIZED_RANGE, REALIZED_QUANTILE_VARIANCE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 1 + m = length(price); + time = linspace(9.5*3600,16*3600,m)'; + timeType = 'seconds'; + samplingType = 'businesstime'; + samplingInterval = 1; + subsamples = 1; + options = realized_options('multiscale'); + case 5 + subsamples = 1; + options = realized_options('multiscale'); + case 6 + options = realized_options('multiscale'); + case 7 + % Nothing + otherwise + error('One, five, six or seven inputs required.') +end +samplingType=lower(samplingType); +timeType=lower(timeType); +[errorMessage, options] = realized_multiscale_variance_parameter_check(price,time,timeType,samplingType,samplingInterval,subsamples,options); + +if ~isempty(errorMessage ) + error(errorMessage) +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +logPrice = log(price); +[filteredLogPrice,filteredTimes] = realized_price_filter(logPrice,time,timeType,samplingType,samplingInterval); +% FIXME: Is m length of returns or of price? +m = length(filteredLogPrice) - 1; + + +if isempty(options.bandwidth) + % Estimate the optimal bandwidth if not provided + [noiseVariance, debiasedNoiseVariance, IQEstimate] = realized_noise_estimate(price, time, timeType, options); + diagnostics.noiseVariance=noiseVariance; + diagnostics.debiasedNoiseVariance=debiasedNoiseVariance; + diagnostics.IQEstimate=IQEstimate; + % Select the correct noise variance estimate + if options.useDebiasedNoise + selectedNoiseVariance = debiasedNoiseVariance; + else + selectedNoiseVariance = noiseVariance; + end + % Compute the bandwidth + m = length(filteredLogPrice) - 1; + % FIXME Bandwidth is wrong + % deriv = 2*(52/35)*IQEstimate*c.^4 - 48/5*c.^(2)*(selectedNoiseVariance*(sqrt(IQEstimate)+selectedNoiseVariance/2))-144*selectedNoiseVariance^2; + % Never consider < 1/sqrt(m) so that BW is always >=1 + if IQEstimate>0 % makes no sense if IQ == 0 + LB = 2/sqrt(m); + % NEver use more than sqrt m + % Comes form Eq. 37 of Zhang assuming that Var(eps^2) = 2 omega^4 + UB = m^(1/2); + c = UB; + UBderiv = 2*(52/35)*IQEstimate*c.^4 - 48/5*c.^(2)*(selectedNoiseVariance*(sqrt(IQEstimate)+selectedNoiseVariance/2))-144*selectedNoiseVariance^2; + for j=1:32 + MP = (UB+LB)/2; + c = MP; + MPderiv = 2*(52/35)*IQEstimate*c.^4 - 48/5*c.^(2)*(selectedNoiseVariance*(sqrt(IQEstimate)+selectedNoiseVariance/2))-144*selectedNoiseVariance^2; + + if sign(MPderiv) == sign(UBderiv) + UB = MP; + UBderiv = MPderiv; + else + LB = MP; + end + end + c = (UB+LB)/2; + options.bandwidth = c*sqrt(m); + else + warning('oxfordRealized:smallBandwidth','IQ Estimate is 0 so optimal bandwidth selection is not possible.') + options.bandwidth = 5; + end +end + +bandwidth = ceil(options.bandwidth); +if bandwidth<2 + warning('oxfordRealized:smallBandwidth','The selected bandwidth is less then 2, and RVMS is not well defined in this case. Setting bandwidth to 2 and proceeding.') + bandwidth = 2; +end +diagnostics.bandwidth = bandwidth; + + + +RVq = zeros(bandwidth,1); +for skip=1:bandwidth + [RVq(skip),count,naturalCount] = overlap_realized_variance(filteredLogPrice,skip); + RVq(skip) = RVq(skip) * (naturalCount / count); +end +% Weights come from Eq. 20 +M = bandwidth; +weights = zeros(M,1); +for i=1:M + weights(i) = 12 * (i / (M^2)) * (i/M - 1/2 - 1/(2*M)) / (1- (1 / M^2)); +end +rvms = weights'*RVq; + +% Subsampled version computed AC0 for multiple starting values, which then leads to different values +% for RVq and the statistic, which can then be averaged + +% Subsampled RVq and RV1 +subsampledLogPrices = realized_subsample(logPrice,time,timeType,samplingType,samplingInterval,subsamples); +RVqs = zeros(subsamples,M); +count = zeros(subsamples,M); +naturalCount = zeros(subsamples,M); +for i=1:subsamples + filteredLogPrice = subsampledLogPrices{i}; + for skip=1:M + [RVqs(i,skip),count(i,skip),naturalCount(i,skip)] = overlap_realized_variance(filteredLogPrice,skip); + end +end +count = sum(count,1); +scale = naturalCount(1,:) ./ count; +RVqs = sum(RVqs,1); +RVq = RVqs .* scale; +RVq = RVq'; +rvmsSS = weights'*RVq; + +end + + +function [rv,count,naturalCount] = overlap_realized_variance(price,skip) + +naturalCount = (length(price)-1)/skip; +m = length(price); +returns = price(2+skip:m) - price(1:m-skip-1); +count = length(returns); +rv = returns' * returns; + +end + + + +function [errorMessage,options] = realized_multiscale_variance_parameter_check(price,time,timeType,samplingType,samplingInterval,subsamples,options) +% Support function for realized_multiscale_variance that does input validation +% +% USAGE: +% [ERRORMESSAGE,OPTIONS] = realized_variance_optimal_sampling_parameter_check(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINVERVAL,OPTIONS) +% +% INPUTS: +% See realized_variance_optimal_sampling +% +% OUTPUT: +% ERRORMESSAGE - String containing a description of the error if one is detected. Empty if no error. +% +% COMMENTS: +% See realized_options for a description of the other fields in OPTIONS +% +% See also REALIZED_VARIANCE_OPTIMAL_SAMPLING + + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 +errorMessage = []; + +if size(price,2)>size(price,1) + price=price'; +end +if size(price,2)>1 + errorMessage = 'PRICE must be a m by 1 vector.'; + return +end +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + errorMessage = 'TIME must be sorted and increasing'; + return +end +if size(time,2)>1 || length(time)~=length(price) + errorMessage = 'TIME must be a m by 1 vector.'; + return +end + +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','unit'}) + errorMessage = 'TIMETYPE must be one of ''wall'', ''seconds'' or ''unit''.'; + return; +end + + +samplingType=lower(samplingType); +if ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform'}) + % Must be a scalar integer + if ~isscalar(samplingInterval) || floor(samplingInterval)~=samplingInterval || samplingInterval<1 + errorMessage = 'SAMPLINGINTERVAL must be a positive integer for the SAMPLINGTYPE selected.'; + return + end +else + if size(samplingInterval,2)>size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + if ~(any(samplingInterval>=t0) && any(samplingInterval<=tT)) + errorMessage = 'At least one sampling interval must be between min(TIME) and max(TIME) when using ''Fixed'' as SAMPLINGTYPE.'; + return + end + if any(diff(samplingInterval)<=0) + errorMessage = 'When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.'; + return + end +end + +% Options + + +% List of flat top kernels +flatTopKernelList = {'bartlett','multiscale','2ndorder','epanechnikov',... + 'cubic','multiscale','5thorder','6thorder','7thorder','8thorder','parzen',... + 'th1','th2','th5','th16'}; + +% List of non flat top kernels +nonFlatTopKernelList = {'nonflatparzen','qs','fejer','thinf','bnhls'}; + +% Combined kernel list +kernelList = [flatTopKernelList nonFlatTopKernelList]; + +% Check fields for valid values +optionsFieldNames = fieldnames(options); +% Insert any missing fiedls +defaultOptions = realized_options('Optimal Sampling'); +defaultFieldNames = fieldnames(defaultOptions); +missingFields = setdiff(defaultFieldNames,optionsFieldNames); +if ~isempty(missingFields) + for i = 1:length(missingFields) + options.(missingFields{i}) = defaultOptions.(missingFields{i}); + end +end + +for i=1:length(optionsFieldNames) + fieldName = optionsFieldNames{i}; + fieldValue = options.(fieldName); + if ischar(fieldValue) + fieldValue = lower(fieldValue); + options.(fieldName) = fieldValue; + end + + switch fieldName + case {'medFrequencyKernel'} + % Member of kernelList + if ~ismember(fieldValue,kernelList) + errorMessage = ['OPTIONS.' fieldName ' must be one of the listed types.']; + return + end + case {'medFrequencyBandwidth'} + % Non-negative scalar + if ~isempty(fieldValue) && ~isnonnegativescalar(fieldValue) + errorMessage = ['OPTIONS.' fieldName ' must a non-negative scalar.']; + return + end + case {'useDebiasedNoise','useAdjustedNoiseCount'} + % Logical or scalar + if ~islogical(fieldValue) && ~ismember(fieldValue,[0 1]) + errorMessage = 'OPTIONS.useDebiasedNoise must be a logical value.'; + return + end + case {'IQEstimationSamplingType','medFrequencySamplingType','noiseVarianceSamplingType'} + % One of the sampling types + if ~ismember(fieldValue,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + errorMessage = ['OPTIONS.' fieldName ' must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.']; + return + end + case {'medFrequencySamplingInterval','noiseVarianceSamplingInterval','IQEstimationSamplingInterval'} + % Non-negative scalar, less that 1 if timeType is unit + if isempty(fieldValue) || ~isnonnegativescalar(fieldValue) + errorMessage = ['OPTIONS.' fieldName ' must be a non-negative scalar between 0 and 1.']; + return + end + if strcmp(timeType,'unit') && fieldValue>1 + errorMessage = ['OPTIONS.' fieldName ' must be less than 1 if TIMETYPE when ''unit''.']; + return + end + end +end + +if ~isempty(subsamples) + if ~isscalar(subsamples) || subsamples<0 || floor(subsamples)~=subsamples + errorMessage = 'SUBSAMPLES must be a non-negative scalar.'; + end +end +end + +function condition = isnonnegativescalar(x) +% Function that returns logical true if that input is a non-empty scalar >=0 +condition = ~isempty(x) && isscalar(x) && x>=0; +end \ No newline at end of file diff --git a/realized/realized_multivariate_kernel.m b/realized/realized_multivariate_kernel.m new file mode 100644 index 0000000..e243b5f --- /dev/null +++ b/realized/realized_multivariate_kernel.m @@ -0,0 +1,495 @@ +function [rmk,diagnostics]=realized_multivariate_kernel(varargin) +% Computes the multivariate version of the realized kernel of BNHLS using the non-flat-top kernels +% and end-point jittering +% +% USAGE: +% [RMK,DIAGNOSTICS] = realized_multivariate_kernel(PRICE01,TIME01,PRICE02,TIME02,...,PRICEN,TIMEN,.. +% TIMETYPE,SAMPLINGINTERVAL,OPTIONS) +% [RMK,DIAGNOSTICS] = realized_multivariate_kernel(PRICES,TIMES,TIMETYPE,SAMPLINGINTERVAL,OPTIONS) +% INPUTS: +% PRICE01 - m01 by 1 vector of high frequency prices +% TIME01 - m01 by 1 vector of times where TIME01(i) corresponds to PRICE01(i) +% PRICE02 - m02 by 1 vector of high frequency prices +% TIME02 - m02 by 1 vector of times where TIME02(i) corresponds to PRICE02(i) +% [N price-time pairing as required, where N can be any integer] +% PRICEN - mN by 1 vector of high frequency prices +% TIMEN - mN by 1 vector of times where TIMEN(i) corresponds to PRICEN(i) +% -or- +% PRICES - Cell array containing prices, e.g. PRICES{1}=PRICE01, +% PRICES{2}=PRICE02, etc. +% TIMES - Cell array containing observation times, e.g. TIMES{1}=TIME01, +% TIMES{2}=TIME02, etc. +% TIMETYPE - String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight on the first day. +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the other types and can be +% applied to data from more than one calendar day +% SAMPLINGINTERVAL - Scalar integer or n by 1 vector which indicates the sampling interval of the +% refresh-time synchronized prices. This value is the multivariate extension +% of the SAMPLINGINTERVAL for 'BusinessTime' sampling in the univariate kernel. +% 1 indicates to use every price. 2 indicates to use every other price, and +% so on. 1 is usually the correct choice. +% OPTIONS - [OPTIONAL] Realized Kernel option structure initialized by calling +% realized_options('Kernel'). See help realized_options for a description of +% available options. +% +% OUTPUTS: +% RMK - Realized covariance estimate +% DIAGNOSTICS - Structure of useful diagnostic information. Fields are +% KERNEL - The kernel used in the RMK +% BANDWIDTH - Number of lags used in the RMK except in the case of an +% infinite lag kernel. +% ADJUSTMENT - De-biasing adjustment for the RK to recognize that less than +% the entire sample was used to compute the 0-lag term +% RTPRICE - Prices used in the RK +% RTTIME - Time stamps of filtered prices used in the RK +% NOISEVARIANCE - Bandi-Russell noise variance estimate. Empty if not needed to +% compute the optimal bandwidth or number of points to jitter +% DEBIASEDNOISEVARIANCE - Bias adjusted estimate of the noise variance +% JITTERLAGS - Present only if the end points are jittered, contains the +% number of points that used to implement the pre-averaging. +% +% COMMENTS: +% The only samplng scheme available is refresh time. Hence the input SAMPLINGTYPE is not defined. +% The only end point treatment is jittering (pre-averaging). This is required to ensure the +% multivariate realized kernels are positive semi-definite. +% +% Calling realized_multivariate_kernel with a single price series: +% [RMK] = realized_multivariate_kernel(PRICE1,TIME1,TIMETYPE,SAMPLINGINTERVAL,OPTIONS) +% +% is the same as calling realized_kernel: +% [RK] = realized_kernel(PRICE1,TIME1,TIMETYPE,'BusinessTime',SAMPLINGINTERVAL,OPTIONS) +% +% EXAMPLES: +% +% See also REALIZED_COVARIANCE, REALIZED_HAYASHI_YOSHIDA, REALIZED_KERNEL, REALIZED_VARIANCE, +% REALIZED_QUANTILE_VARIANCE, REALIZED_RANGE + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking and Parsing +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin<4 + error('At least 4 inputs required') +end + +% Handle case where cell array is used to hold prices and times +if iscell(varargin{1}) + k = length(varargin{1}); + m = length(varargin)-2; + temp = cell(1,2*k+m); + for i=1:k + temp{2*i-1} = varargin{1}{i}; + temp{2*i} = varargin{2}{i}; + end + for i=1:m + temp{2*k+i} = varargin{2+i}; + end + varargin = temp; +end +% Check inputs +[errorMessage, options, numPrices, timeType, samplingInterval] = realized_multivariate_kernel_parameter_check(varargin{:}); + +if ~isempty(errorMessage ) + error(errorMessage) +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + +% 0. Quick filter using refresh time to estimate the number of data points that will be available +rtPrice = realized_refresh_time(timeType,varargin{1:2*numPrices}); +if samplingInterval~=1 + rtPrice=rtPrice(1:samplingInterval:size(rtPrice,1),:); +end +nMax = size(rtPrice(1:samplingInterval:size(rtPrice,1),:),1); + +% 1. Determine optimal jitter and jitter each series [if not provided] +% and +% 2. Determine optimal number of lags for each series [if not provided] +options.filteredN = nMax; + +if isempty(options.jitterLags) && isempty(options.bandwidth) + % Need both + bandwidth = zeros(numPrices ,1); + jitterLags = zeros(numPrices ,1); + noiseVariance = zeros(numPrices ,1); + IQEstimate = zeros(numPrices ,1); + for i=1:numPrices + price = varargin{2*(i-1)+1}; + time = varargin{2*i}; + + [noiseVariance(i), debiasedNoiseVariance, IQEstimate(i)] = realized_noise_estimate(price, time, timeType, options); + bandwidth(i) = realized_kernel_bandwidth(noiseVariance(i), IQEstimate(i), options); + + if bandwidth>(.25*nMax) + bandwidth = round(.25*nMax); + warning('oxfordRealized:realizedKernelLength','The estimated bandwidth requires a lag length larger than 25%% of the available data. Bandwidth has been truncated to 25%% of data.'); + end + jitterLags(i) = realized_kernel_jitter_lag_length(noiseVariance(i), IQEstimate(i), kernel, nMax); + jitterLags(i) = max(jitterLags(i),1); + end + options.bandwidth = round(mean(bandwidth)); +elseif isempty(options.jitterLags) && ~isempty(options.bandwidth) + % Need jitterLags + jitterLags = zeros(numPrices ,1); + noiseVariance = zeros(numPrices ,1); + IQEstimate = zeros(numPrices ,1); + for i=1:numPrices + price = varargin{2*(i-1)+1}; + time = varargin{2*i}; + + [noiseVariance(i), debiasedNoiseVariance, IQEstimate(i)] = realized_noise_estimate(price, time, timeType, options); + + jitterLags(i) = realized_kernel_jitter_lag_length(noiseVariance(i), IQEstimate(i), kernel, nMax); + jitterLags(i) = max(jitterLags(i),1); + end +elseif ~isempty(options.jitterLags) && isempty(options.bandwidth) + bandwidth = zeros(numPrices ,1); + jitterLags = zeros(numPrices ,1); + noiseVariance = zeros(numPrices ,1); + IQEstimate = zeros(numPrices ,1); + for i=1:numPrices + price = varargin{2*(i-1)+1}; + time = varargin{2*i}; + + [noiseVariance(i), debiasedNoiseVariance, IQEstimate(i)] = realized_noise_estimate(price, time, timeType, options); + bandwidth(i) = realized_kernel_bandwidth(noiseVariance(i), IQEstimate(i), options); + + if bandwidth>(.25*nMax) + bandwidth = round(.25*nMax); + warning('oxfordRealized:realizedKernelLength','The estimated bandwidth requires a lag length larger than 25%% of the available data. Bandwidth has been truncated to 25%% of data.'); + end + end + options.bandwidth = round(mean(bandwidth)); + jitterLags = ones(numPrices,1)*options.jitterLags; +end + +% Do the jittering +for i=1:numPrices + price = varargin{2*(i-1)+1}; + time = varargin{2*(i-1)+2}; + m = size(price,1); + p0 = mean(price(1:jitterLags(i))); + p1 = mean(price(m-jitterLags(i)+1:m)); + t0 = time(ceil(mean(1:jitterLags(i)))); + t1 = time(floor(mean(m-jitterLags(i)+1:m))); + price = [p0;price(jitterLags(i)+1:m-jitterLags(i));p1]; + time = [t0;time(jitterLags(i)+1:m-jitterLags(i));t1]; + varargin{2*(i-1)+1} = price; + varargin{2*(i-1)+2} = time; +end +% 3. Put into refresh time +[rtPrice,rtTime] = realized_refresh_time(timeType,varargin{1:2*numPrices}); + +if samplingInterval~=1 + rtPrice=rtPrice(1:samplingInterval:size(rtPrice,1),:); +end +% 4. Compute the weights +weights = realized_kernel_weights(options); +% 5. Compute the kernel +rtReturns = diff(log(rtPrice)); +rmk = realized_multivariate_kernel_core(rtReturns,weights); + +diagnostics.kernel = options.kernel; +diagnostics.bandwidth = options.bandwidth; +diagnostics.jitterLags = jitterLags; +diagnostics.weights = weights; +diagnostics.rtPrice = rtPrice; +diagnostics.rtTime = rtTime; + + + + + +function rmk = realized_multivariate_kernel_core(returns, weights) +% Realized Multivariate Kernel core routine that computes the value of a multivariate realized kernel +% given a set of returns and weights. +% +% USAGE: +% [RMK] = realized_kernel_core(RETURNS,WEIGHTS) +% +% INPUTS: +% RETURNS - m by 1 column vector of returns +% WEIGHTS - H by 1 column vector of kernel weights corresponding to +% lags 1, 2, ..., H. H should be much smaller than m +% +% OUTPUTS: +% RMK - Realized multivariate kernel value +% +% COMMENTS: +% This is a helper function for REALIZED_MULTIVARIATE_KERNEL +% +% See also REALIZED_MULTIVARIATE_KERNEL, REALIZED_KERNEL, REALIZED_PRICE_FILTER, +% REALIZED_KERNEL_WEIGHTS, REALIZED_KERNEL_SELECT_LAG_LENGTH, REALIZED_COVARIANCE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 7/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=2 + error('Two inputs required.') +end + +if size(weights,2)>1 + error('WEIGHTS must be a H by 1 vector.') +end + +% Get the number of returns +[m,k]=size(returns); +if length(weights)>=m + warning('oxfordRealized:realizedKernelLength','The length of WEIGHTS is longer than the length of RETURNS.\n The weights are being truncated at N-1 where N is the number of returns') + weights = weights(1:m-1); +elseif length(weights)> .1*length(returns) + warning('oxfordRealized:realizedKernelLength','The number of WEIGHTS may be excessive. Consider using a smaller kernel.') +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Get the size of the kernel +H=length(weights); + + +% Use all returns when computing autocovariances +gammaH = zeros(k,k,H); +% Loop and compute the values for gamma +for i=1:H + returnsMinus = returns(1:m-i,:); + returnsPlus = returns(i+1:m,:); + gammaH(:,:,i) = returnsMinus' * returnsPlus; +end +% Compute the 0-lag gamma using all returns +gamma0 = returns' * returns; + +% Construct the kernel +rmk = gamma0; +if ~isempty(weights) + for j=1:length(weights) + rmk = rmk + weights(j)*(gammaH(:,:,j)+gammaH(:,:,j)'); + end +else + warning('oxfordRealized:realizedKernelLength','The number of lags used was 0.'); +end + + + + + + + + + + + + + + + + + + + + + + + + +function [errorMessage, options, numPrices, timeType, samplingInterval] = realized_multivariate_kernel_parameter_check(varargin) +% Support function for realized_multivariate_kernel that does input validation +% +% USAGE: +% [ERRORMESSAGE,OPTIONS] = realized_kernel_parameter_check(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINVERVAL,OPTIONS) +% +% INPUTS: +% See realized_kernel +% +% OUTPUT: +% ERRORMESSAGE - String containing a description of the error if one is detected. Empty if no +% error. +% OPTIONS - A realized_kernel options structure with the additional field +% filteredN - Number of observations that are used to compute the kernel. This is +% needed for computing the optimal bandwidth. +% +% COMMENTS: +% See realized_options for a description of the other fields in OPTIONS +% +% See also REALIZED_KERNEL, REALIZED_OPTIONS + + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +% initialized errorMessage +errorMessage = []; + +% Determine the number of prices and times +k = length(varargin); +if k/2~=floor(k/2) + options = varargin{k}; + timeType = varargin{k-2}; + samplingInterval = varargin{k-1}; + numPrices = (k-3)/2; +else + options = realized_options('Multivariate Kernel'); + timeType = varargin{k-1}; + samplingInterval = varargin{k}; + numPrices = (k-2)/2; +end + + + + + +% Prices and times +for i=1:numPrices + price = varargin{2*i-1}; + time = varargin{2*i}; + if size(price,2)>size(price,1) + price=price'; + end + if size(price,2)>1 + errorMessage = ['PRICE series ' num2str(i) ' must be a m(i) by 1 vector.']; + return + end + + % Time + if size(time,2)>size(time,1) + time=time'; + end + if any(diff(time)<0) + errorMessage = ['TIME for series ' num2str(i) ' must be sorted and increasing']; + return + end + if size(time,2)>1 || length(time)~=length(price) + errorMessage = ['TIME for series ' num2str(i) ' must be a m(i) by 1 vector the same size as PRICE series (i).']; + return + end +end + +% TimeType +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','unit'}) + errorMessage = 'TIMETYPE must be one of ''wall'', ''seconds'' or ''unit''.'; + return +end + + +if samplingInterval<1 || ~isscalar(samplingInterval) + errorMessage = 'SAMPLINGINTERVAL must be a positive integer (usually 1).'; + return +end + +% Options + +% List of flat top kernels +flatTopKernelList = {'bartlett','twoscale','2ndorder','epanechnikov',... + 'cubic','multiscale','5thorder','6thorder','7thorder','8thorder','parzen',... + 'th1','th2','th5','th16'}; + +% List of non flat top kernels +nonFlatTopKernelList = {'nonflatparzen','qs','fejer','thinf','bnhls'}; + +% Combined kernel list +kernelList = [flatTopKernelList nonFlatTopKernelList]; + +% Check fields for valid values +optionsFieldNames = fieldnames(options); +% Insert any missing fiedls +defaultOptions = realized_options('Kernel'); +defaultFieldNames = fieldnames(defaultOptions); +missingFields = setdiff(defaultFieldNames,optionsFieldNames); +if ~isempty(missingFields) + for i = 1:length(missingFields) + options.(missingFields{i}) = defaultOptions.(missingFields{i}); + end +end + +for i=1:length(optionsFieldNames) + fieldName = optionsFieldNames{i}; + fieldValue = options.(fieldName); + if ischar(fieldValue) + fieldValue = lower(fieldValue); + options.(fieldName) = fieldValue; + end + + switch fieldName + case 'kernel' + % Member of kernelList + if ~ismember(fieldValue,nonFlatTopKernelList) + errorMessage = ['OPTIONS.' fieldName ' must be one of the listed types.']; + return + end + case 'medFrequencyKernel' + % Member of kernelList + if ~ismember(fieldValue,kernelList) + errorMessage = ['OPTIONS.' fieldName ' must be one of the listed types.']; + return + end + case {'bandwidth','medFrequencyBandwidth'} + % Non-negative scalar + if ~isempty(fieldValue) && ~isnonnegativescalar(fieldValue) + errorMessage = ['OPTIONS.' fieldName ' must a non-negative scalar.']; + return + end + case 'endTreatment' + % String + if ~ismember(fieldValue,{'jitter'}) + errorMessage = 'OPTIONS.endTreatment must be ''Jitter''.'; + return + end + case {'jitterLags','maxBandwidth'} + % Non-negative scalar integer + if ~isempty(fieldValue) && ~isnonnegativescalarinteger(fieldValue) + errorMessage = ['OPTIONS.' fieldName ' must be a non-negative scalar integer.']; + return + end + case {'useDebiasedNoise','useAdjustedNoiseCount'} + % Logical or scalar + if ~islogical(fieldValue) && ~ismember(fieldValue,[0 1]) + errorMessage = 'OPTIONS.useDebiasedNoise must be a logical value.'; + return + end + case 'maxBandwidthPerc' + % Scalar 0<=fieldvalue<=1 + if ~isempty(fieldValue) && ~isnonnegativescalar(fieldValue) && fieldValue>1 + errorMessage = 'OPTIONS.maxBandwidthPerc must be a non-negative scalar between 0 and 1.'; + return + end + case {'IQEstimationSamplingType','medFrequencySamplingType','noiseVarianceSamplingType'} + % One of the sampling types + if ~ismember(fieldValue,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + errorMessage = ['OPTIONS.' fieldName ' must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.']; + return + end + case {'medFrequencySamplingInterval','noiseVarianceSamplingInterval','IQEstimationSamplingInterval'} + % Non-negative scalar, less that 1 if timeType is unit + if isempty(fieldValue) || ~isnonnegativescalar(fieldValue) + errorMessage = ['OPTIONS.' fieldName ' must be a non-negative scalar between 0 and 1.']; + return + end + if strcmp(timeType,'unit') && fieldValue>1 + errorMessage = ['OPTIONS.' fieldName ' must be less than 1 if TIMETYPE when ''unit''.']; + return + end + end +end + + + +function condition = isnonnegativescalarinteger(x) +% Function that returns logical true if that input is a non-empty, scalar integer >=0 +condition = ~isempty(x) && isscalar(x) && x>=0 && x==floor(x); + + +function condition = isnonnegativescalar(x) +% Function that returns logical true if that input is a non-empty scalar >=0 +condition = ~isempty(x) && isscalar(x) && x>=0; diff --git a/realized/realized_noise_estimate.m b/realized/realized_noise_estimate.m new file mode 100644 index 0000000..86a4a8f --- /dev/null +++ b/realized/realized_noise_estimate.m @@ -0,0 +1,121 @@ +function [noiseVariance, debiasedNoiseVariance, IQEstimate] = realized_noise_estimate(price, time, timeType, options) +% Estimation of the optimal bandwidth to use when estimating the quadratic variation using a Realized Kernel +% +% USAGE: +% [NOISEESTIMATE,RAWNOISEESTIMATE,IQESTIMATE] = realized_kernel_select_bandwidth(PRICE,TIME,TIMETYPE,OPTIONS) +% +% INPUTS: +% PRICE - m by 1 vector of prices +% TIME - m by 1 vector of times where TIME(i) corresponds to PRICE(i) +% TIMETYPE - String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight on the first day +% 'unit' Unit normalized date format, e.g. .1, .234, .9. Unit normalized times are +% more general than the other types and can be applied to data from more than one +% calendar day +% OPTIONS - Realized kernel options structure. See help realized_kernel_options +% +% OUTPUTS: +% NOISEVARIANCE - Bandi-Russel noise variance estimate +% DEBIASEDNOISEVARIANCE - Debiased Bandi-Russel noise variance estimate using the adjustment of BNHLS +% IQESTIMATE - An estimate of the lower bound of the IQ based on low-freuqency returns +% +% COMMENTS: +% This is a helper function for REALIZED_KERNEL. See Barndorf-Nielsen, Hansen, Lunde and Shephard +% (2008) for details about the optimal selection of bandwidth +% +% See also REALIZED_KERNEL, REALIZED_PRICE_FILTER, REALIZED_KERNEL_WEIGHTS +% REALIZED_KERNEL_SELECT_LAG_LENGTH, REALIZED_VARIANCE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=4 + error('Seven inputs required.') +end +if size(price,2)>size(price,1) + price=price'; +end +if size(price,2)>1 + error('PRICE must be a m by 1 vector.') +end +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + error('TIME must be sorted and increasing') +end +if size(time,2)>1 || length(time)~=length(price) + error('TIME must be a m by 1 vector.') +end +time = double(time); +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','matlab'}) + error('TIMETYPE must be one of ''wall'', ''seconds'' or ''Matlab''.'); +end + +% List of flat top kernels +flatTopKernelList = {'bartlett','twoscale','2ndorder','epanechnikov',... + 'cubic','multiscale','5thorder','6thorder','7thorder','8thorder','parzen',... + 'th1','th2','th5','th16'}; + +% List of non flat top kernels +nonFlatTopKernelList = {'nonflatparzen','qs','fejer','thinf','bnhls'}; + +% Combined kernel list +kernelList = [flatTopKernelList nonFlatTopKernelList]; + +if ~isfield(options,'medFrequencyKernel') || ~ismember(options.medFrequencyKernel,kernelList) + error('KERNEL must be a field of OPTIONS and one of the listed types.') +end + +medFrequencySamplingType = options.medFrequencySamplingType; +medFrequencySamplingInterval = options.medFrequencySamplingInterval; +medFrequencyKernel = options.medFrequencyKernel; +medFrequencyBandwidth = options.medFrequencyBandwidth; +if ~isscalar(medFrequencySamplingInterval) || floor(medFrequencySamplingInterval)~=medFrequencySamplingInterval || medFrequencySamplingInterval<=0 + error('MEDIUMFREQUENCYTIME must be a postive integer scalar value.'); +end + +IQEstimationSamplingType = options.IQEstimationSamplingType; +IQEstimationSamplingInterval = options.IQEstimationSamplingInterval; +if ~isscalar(IQEstimationSamplingInterval) || floor(IQEstimationSamplingInterval)~=IQEstimationSamplingInterval || IQEstimationSamplingInterval<=0 + error('LOWFREQUENCYTIME must be a postive integer scalar value.'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% To compute the "optimal" bandwidth an estimate of the noise and the QV using low frequency data +lowFrequencyRealizedVariance = realized_variance(price,time, timeType , IQEstimationSamplingType, IQEstimationSamplingInterval); + +noiseVarianceSamplingType = options.noiseVarianceSamplingType; +noiseVarianceSamplingInterval = options.noiseVarianceSamplingInterval; + +% Compute the noiseVariance using the debiased version of Bandi-Russell, using all prices +noiseVariance = realized_variance(price, time, timeType , noiseVarianceSamplingType , noiseVarianceSamplingInterval); +% Compute the effective 'n' to use in the Bandi-Russel estimator +noiseFilteredPrice = realized_price_filter(price, time, timeType , noiseVarianceSamplingType , noiseVarianceSamplingInterval); +if options.useAdjustedNoiseCount + % Only count the number of non-zero returns + n = sum(diff(noiseFilteredPrice)~=0); +else + n = length(noiseFilteredPrice) - 1; +end +noiseVariance = noiseVariance/(2*n); + +% Require a realized kernel estimate to adjust the variance +medFrequencyOptions = realized_options('kernel'); +medFrequencyOptions.kernel = medFrequencyKernel; +medFrequencyOptions.bandwidth = medFrequencyBandwidth; +medFrequencyOptions.endTreatment = 'stagger'; + +medFreuqencyRealizedKernel = realized_kernel(price, time, timeType, medFrequencySamplingType, medFrequencySamplingInterval, medFrequencyOptions); +medFrequencyRealizedVariance = realized_variance(price,time, timeType , medFrequencySamplingType, medFrequencySamplingInterval); +% Use the BNHLS corrected noise estimate +debiasedNoiseVariance = exp( log(noiseVariance) - medFreuqencyRealizedKernel/medFrequencyRealizedVariance); +IQEstimate = lowFrequencyRealizedVariance^2; \ No newline at end of file diff --git a/realized/realized_options.m b/realized/realized_options.m new file mode 100644 index 0000000..a5641d3 --- /dev/null +++ b/realized/realized_options.m @@ -0,0 +1,207 @@ +function options = realized_options(realizedFunction) +% Returns an option structure for use with realized_kernel and realized_variance_optimal_sampling containing the default values. +% +% USAGE: +% [OPTIONS] = realized_options(REALIZEDFUNCTION) +% +% INPUTS: +% REALIZEDFUNCTION - String containing the name of estimator being used. Currently supported: +% 'Kernel' - Realized kernel estimation (realized_kernel) +% 'Multivariate Kernel' - Realized kernel estimation (realized_multivariate_kernel) +% 'Optimal Sampling' - Realized variance using Bandi-Russell optimal sampling +% (realized_variance_optimal_sampling) +% 'Twoscale' - Two-scale Realized variance +% 'Multiscale' - Multisclae Realized variance +% 'QMLE' - QMLE estimation of QV +% OUTPUT: +% OPTIONS - A structure that may include the fields (default values in parentheses) +% kernel - One of the supported kernels ('nonflatparzen') +% Non-flat-top, weakly positive, n^(1/5) rate: +% 'nonflatparzen' [RECOMMENDED] Parzen kernel applied to non-flat-top case +% 'qs' Quadratic Spectral +% 'fejer' Fejer kernel +% 'thinf' Tukey-Hanning kernel with infinite lag order +% 'bnhls' Kernel proposed by Barndorf-Neilsen, Hansen, Lunde and Shephard +% Flat-top, n^(1/4) rate: +% 'parzen' Parzen's kernel +% 'th1' Tukey-Hanning kernel with power 1 +% 'th2' Tukey-Hanning kernel with power 2 +% 'th5' Tukey-Hanning kernel with power 5 +% 'th16' Tukey-Hanning kernel with power 16 +% 'cubic','multiscale' 3rd order (cubic) kernel, which is asymptotically +% equivalent to multiscale realized variance +% '5thorder' 5th order Kernel +% '6thorder' 6th order Kernel +% '7thorder' 7th order Kernel +% '8thorder' 8th order Kernel +% Flat-top, n^(1/6) rate: +% 'bartlett','twoscale' Bartlett kernel, which is asymptotically equivalent to the +% two-scale estimator +% '2ndorder' 2nd order (quadratic) kernel +% 'epanechnikov' Epanechnikov kernel +% endTreatment - String value containing 'Jitter' or 'Stagger' ('Jitter') +% 'Jitter'ing the end points means that the first q and the last q observations are +% pre-averaged before computing the kernel. This is needed (theoretically) to +% remove end effects. Once the end points are jittered the kernel is computed using +% all data to compute every realized autocovariance. NOTE: 'Jitter' must be used if +% a non-flat top kernel is used. +% 'Stagger' does not pre-average but uses a kernel computed from realized +% autocovariances computed from non-overlapping returns. +% jitterLags - Number of lags to use if 'Jitter' is selected in endTreatment (2). If +% empty ([]) the optimal number of end points to jitter is selected automatically. +% maxBandwidthPerc - Non-negative scalar between 0 and 1 maximum +% bandwidth to use as a percentage of the number of observations (.25) +% maxBandwidth - Non-negative scalar maximum bandwidth to use as an absolut number ([]) +% bandwidth - Non-negative scale bandwidth to use when computing the realized kernel ([]). +% If empty the optimal bandwidth is estimated using a plug-in estimator. +% +% The remaining fields are only used if bandwidth or jitterLags is estimated. +% (i.e. OPTIONS.bandwidth = [] or OPTIONS.jitterLags = []) +% useDebiasedNoise - Logical value indicating whether to use debiased noise or not +% when estimating the optimal bandwidth (false) +% useAdjustedNoiseCount - Logical value indicating whether the count of the number of +% observations used in the noise estimate should include only non-zero returns (true) +% medFrequencySamplingType - Sampling type to use when computing the realized +% variance and kernel used in the debiased noise estimate ('BusinessUniform'). See +% realized_price_filter for a description of the avilable sampling types +% medFrequencySamplingInterval - Sampling interval to use when computing the realized +% variance and kernel used in the debiased noise estimate (390). See +% realized_price_filter for the precise interpretation of sampling interval which +% depends on the selected sampling type. +% medFrequencyKernel - Kernel to use when computing the debiased noise estimated ('parzen') +% medFrequencyBandwidth - Bandwidth to use with medFrequencyKernel (5) +% noiseVarianceSamplingType - Sampling type to use when computing the realized +% variance used in the noise estimator ('BusinessUniform'). +% noiseVarianceSamplingInterval - Sampling interval to use when computing the realized +% variance used in the noise estimator (120). +% IQEstimationSamplingType - Sampling type to use when computing the realized +% variance used in the IQ estimator ('BusinessUniform') +% IQEstimationSamplingInterval - Sampling interval to use when computing the realized +% variance used in the IQ estimator (39) +% +% COMMENTS: +% These values have been calibrated to use with liquid NYSE TAQ data. It may be necessary to +% modify these values if computing realized kernels on illiquid data or on data which trades over +% interval significantly different than 6.5 hours (such as 24-hour markets or where the market +% is closed for part of the day) +% +% Relevant options for each function: +% | Realized | Multivariate | Optimal | Twoscale, | QMLE +% | Kernel | Kernel | Sampling | Multiccale | +% | | | | | +% kernel | x | x | | | +% endTreatment | x | x | | | +% jitterLags | x | x | | | +% maxBandwidthPerc | x | x | | x | +% maxBandwidth | x | x | | x | +% bandwidth | x | x | | x | +% useDebiasedNoise | x | x | x | x | +% useAdjustedNoiseCount | x | x | x | x | +% medFrequencySamplingType | x | x | x | x | x +% medFrequencySamplingInterval | x | x | x | x | x +% medFrequencyKernel | x | x | x | x | +% medFrequencyBandwidth | x | x | x | x | +% noiseVarianceSamplingType | x | x | x | x | x +% noiseVarianceSamplingInterval | x | x | x | x | x +% IQEstimationSamplingType | x | x | x | x | +% IQEstimationSamplingInterval | x | x | x | x | +% +% Note: Optimal Sampling uses default values of noiseVarianceSamplingType = 'BusinessTime' and +% noiseVarianceSamplingInterval = 1 +% +% EXAMPLE: +% % Generate the default options for estimating Realized Kernels +% options = realized_options('kernel') +% +% See also REALIZED_KERNEL, REALIZED_VARIANCE_OPTIMAL_SAMPLING, REALIZED_TWOSCALE_VARIANCE, +% REALIZED_MULTISCALE_VARIANCE, REALIZED_QMLE_VARIANCE + + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin>1 + error('0 or 1 input required.') +end +if nargin==0 + realizedFunction = 'kernel'; +end +realizedFunction = lower(realizedFunction); +if ~ismember(realizedFunction,{'kernel','optimal sampling','twoscale','multiscale','multivariate kernel','qmle'}) + error('REALIZEDFUNCTION must be one of the listed types.') +end +%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%% + + +% Kernel +options.kernel = 'nonflatparzen'; +% End Treatment +options.endTreatment = 'jitter'; +% Max bandwidth percentage of observations +options.maxBandwidthPerc = .25; +% Max bandwidth (absolute) +options.maxBandwidth = []; +% Jitter Lags +options.jitterLags = 2; +% Bandwidth +options.bandwidth = []; +% These options only affect the estimation of bandwdith +% Use debiased noise +options.useDebiasedNoise = false; +% Use adjusted count +options.useAdjustedNoiseCount = true; +% Medium Frequency Sampling Type +options.medFrequencySamplingType = 'BusinessUniform'; +% Medium Frequency Sampling Type +options.medFrequencySamplingInterval = 390; +% Medium Frequency Kernel +options.medFrequencyKernel = 'parzen'; +% Medium Frequency Bandwidth +options.medFrequencyBandwidth = 5; +% Noise Variance Sampling Type +options.noiseVarianceSamplingType = 'BusinessUniform'; +% Noise Variance Sampling Interval +options.noiseVarianceSamplingInterval = 120; +% IQ Estimation Sampling Type +options.IQEstimationSamplingType = 'BusinessUniform'; +% IQ Estimation Sampling Interval +options.IQEstimationSamplingInterval = 39; + + +% Remove any unneeded fields +switch realizedFunction + case {'kernel','multivariate kernel'} + fieldList = {'kernel','endTreatment','jitterLags','maxBandwidthPerc','maxBandwidth',... + 'bandwidth','useDebiasedNoise','useAdjustedNoiseCount','medFrequencySamplingType',... + 'medFrequencySamplingInterval','medFrequencyKernel','medFrequencyBandwidth',... + 'noiseVarianceSamplingType','noiseVarianceSamplingInterval','IQEstimationSamplingType',... + 'IQEstimationSamplingInterval'}; + case {'optimal sampling','twoscale','multiscale'} + fieldList = {'bandwidth','useDebiasedNoise','useAdjustedNoiseCount','medFrequencySamplingType',... + 'medFrequencySamplingInterval','medFrequencyKernel','medFrequencyBandwidth',... + 'noiseVarianceSamplingType','noiseVarianceSamplingInterval','IQEstimationSamplingType',... + 'IQEstimationSamplingInterval'}; + options.noiseVarianceSamplingType = 'BusinessTime'; + options.noiseVarianceSamplingInterval = 1; + options.useAdjustedNoiseCount = false; + case {'qmle'} + fieldList = {'medFrequencySamplingType','medFrequencySamplingInterval',... + 'noiseVarianceSamplingType','noiseVarianceSamplingInterval'}; + options.noiseVarianceSamplingType = 'BusinessTime'; + options.noiseVarianceSamplingInterval = 1; +end + + +fields = fieldnames(options); +for i=1:length(fields) + if ~ismember(fields(i),fieldList) + options = rmfield(options,fields(i)); + end +end + diff --git a/realized/realized_price_filter.m b/realized/realized_price_filter.m new file mode 100644 index 0000000..51b3e16 --- /dev/null +++ b/realized/realized_price_filter.m @@ -0,0 +1,281 @@ +function [filteredPrice,filteredTime,actualTime] = realized_price_filter(price,time,timeType,samplingType,samplingInterval) +% Price filtering for computing realized variances and other +% high-frequency price based returns +% +% USAGE: +% [FILTEREDPRICE,FILTEREDTIME,ACTUALTIME] = realized_price_filter(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL) +% +% INPUTS: +% PRICE - m by 1 column vector of prices +% TIME - m by 1 column vector of times corresponding to PRICE. +% Must be sorted and increasing. +% TIMETYPE - String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS, e.g. 101543 or 153217 +% 'seconds' Time measures in seconds past midnight. +% TIME must satisfy 0<=TIME<86400 +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the +% other types and can be applied to data from more +% than one calendar day +% SAMPLINGTYPE - String describing the type of sampling to use when +% filtering PRICE +% 'CalendarTime' - Sample in calendar time using +% observations separated by SAMPLINGINTERVAL +% seconds. If TIMETYPE is 'unit', +% SAMPLINGINTERVAL must be between 0 and 1 and +% represents the fraction of the sample to skip +% when sampling. +% 'CalendarUniform' - Sample in calendar time using +% SAMPLINGINTERVAL observations spread uniformly +% between TIME(1) and TIME(m) +% 'BusinessTime' - Sample in business (tick) time +% using observation separated by SAMPLINGINTERVAL +% ticks +% 'BusinessUniform' - Sample in business (tick) +% time using observations uniformly spaced in +% business time. +% 'Fixed' - Sample at specific points in time. When +% using fixed, SAMPLINGINTERVAL must be a n by 1 vector +% of times with the same TIMETYPE as TIME (i.e. +% seconds if TIME is in seconds) +% SAMPLINGINTERVAL - Scalar integer or n by 1 vector whose meaning depends on the +% selected SAMPLINGTYPE +% +% OUTPUTS: +% FILTEREDPRICE - n by 1 vector of filtered prices. n depends on +% SAMPLINGTYPE as well as the data +% FILTEREDTIME - n by 1 vector of sampling times corresponding to +% the chosen sampling scheme +% ACTUALTIME - n by 1 vector. ACTUALTIME(i) provides the actual +% observation time that was used when sampling at FILTEREDTIME(i) +% +% +% COMMENTS: +% This is a helper function for REALIZED_KERNEL. Last price +% interpolation is always used. If SAMPLINGTYPE is 'Fixed' then any +% requested samples before the first observation will be back filled +% with PRICE(1). An indicator for back filled values can be constructed +% using ACTUALTIME>FILTEREDTIME +% +% EXAMPLES: +% % 5-minute prices +% FILTEREDPRICE = realized_price_filter(PRICE,TIME,'wall','CalendarTime',300) +% +% % 79 prices spread uniformly in calendar time +% FILTEREDPRICE = realized_price_filter(PRICE,TIME,'wall','CalendarUniform',79) +% +% % 20-tick returns +% FILTEREDPRICE = realized_price_filter(PRICE,TIME,'wall','CalendarUniform',79) +% +% % 391 prices spread uniformly in business time +% FILTEREDPRICE = realized_price_filter(PRICE,TIME,'wall','CalendarUniform',79) +% +% % 5-minute prices coresponding to 9:30:00, 9:35:00, ... +% sampleTimes = seconds2wall(wall2seconds(93000):300:wall2seconds(160000))'; +% FILTEREDPRICE = realized_price_filter(PRICE,TIME,'wall','Fixed',sampleTimes) +% +% % .05-calendar time sampling when using unit times +% TIME = wall2unit(TIME,min(TIME),max(TIME)); +% FILTEREDPRICE = realized_price_filter(PRICE,TIME,'unit','CalendarTime',.05) +% +% +% See also REALIZED_KERNEL, REALIZED_KERNEL_CORE, REALIZED_KERNEL_WEIGHTS +% REALIZED_KERNEL_SELECT_LAG_LENGTH, REALIZED_VARIANCE + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 1 Date: 5/1/2008 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +if nargin~=5 + error('Five inputs required.') +end +if size(price,2)>size(price,1) + price=price'; +end +if size(price,2)>1 + error('PRICE must be a m by 1 vector.') +end +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + error('TIME must be sorted and increasing') +elseif any(diff(time)==0) + warning('oxfordRealized:realizedPriceFilter','TIME contains multiple entries with the same value. This creates an ambiguity and FILTEREDPRICE will contain the last price if TIME does not only unique elements.') +end +if size(time,2)>1 || length(time)~=length(price) + error('TIME must be a m by 1 vector.') +end +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','unit'}) + error('TIMETYPE must be one of ''wall'', ''seconds'' or ''unit''.'); +end +% Inserted to protect against inputing integer times +time = double(time); + +samplingType=lower(samplingType); +if ~ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + error('SAMPLINGTYPE must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.'); +end + +m=size(price,1); +t0Original=time(1); +tTOriginal=time(m); +if ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform'}) + % Must be a scalar integer, unless using unit times + if (~isscalar(samplingInterval) || floor(samplingInterval)~=samplingInterval || samplingInterval<1) && ~strcmp(timeType,'unit') + error('SAMPLINGINTERVAL must be a positive integer for the SAMPLINGTYPE selected.') + end +else + if size(samplingInterval,2)>size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + if ~(any(samplingInterval>=t0Original) && any(samplingInterval<=tTOriginal)) + error('At least one sampling interval must be between min(TIME) and max(TIME) when using ''Fixed'' as SAMPLINGTYPE.') + end + if any(diff(samplingInterval)<=0) + error('When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.') + end +end + +if strcmp(timeType,'unit') && strcmp(samplingType,'calendartime') + % samplingInterval must be between 0 and 1 + if samplingInterval>1 + error('When TIMETYPE is ''unit'' and SAMPLINGTYPE is ''CalendarTime'', SAMPLINGINTERVAL must also be in ''unit'' terms, and so must be between 0 and 1') + end +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +% Get the size of the price +m=size(price,1); + +% Convert times +if strcmp(samplingType,'fixed') + time0 = min(samplingInterval); + time1 = max(samplingInterval); +else + time0 = min(time); + time1 = max(time); +end +if strcmp(timeType,'wall') + time = wall2unit(time,time0,time1); +elseif strcmp(timeType,'seconds') + time = seconds2unit(time,time0,time1); +end +% If fixed convert these times as well +if strcmp(samplingType,'fixed') + if strcmp(timeType,'wall') + samplingInterval = wall2unit(samplingInterval,time0,time1); + elseif strcmp(timeType,'seconds') + samplingInterval = seconds2unit(samplingInterval,time0,time1); + end +end + + +% Get the first and last time +t0=time(1); +tT=time(m); +% Switch based on the cases +switch samplingType + case 'calendartime' + % If calendar time + % Convert sampling interval to be a fraction of a period + % Unit strides + if strcmp(timeType,'wall') + timeBase = wall2seconds([time0 time1]); + samplingInterval = samplingInterval/diff(timeBase); + elseif strcmp(timeType,'seconds') + samplingInterval = samplingInterval/(time1-time0); + end + filteredTime=(t0:samplingInterval:tT)'; + % Append the final observation + if ~ismember(tT,filteredTime) + filteredTime=[filteredTime; tT]; + end + % Compute the filtered prices + [filteredPrice,actualTime]=fasttimefilter(price,time,filteredTime); + case 'calendaruniform' + % Sampling interval contains the number of samples + % Uniform spacing + filteredTime=linspace(t0,tT,samplingInterval)'; + % Compute the filtered prices + [filteredPrice,actualTime]=fasttimefilter(price,time,filteredTime); + case 'businesstime' + indices=(1:samplingInterval:m)'; + if ~ismember(m,indices) + indices=[indices;m]; + end + filteredPrice=price(indices); + filteredTime=time(indices); + actualTime = filteredTime; + case 'businessuniform' + % Sampling interval contains the number of samples + indices=floor(linspace(1,m,samplingInterval)); + filteredPrice=price(indices); + filteredTime=time(indices); + actualTime = filteredTime; + case 'fixed' + filteredTime = samplingInterval; + % Compute the filtered prices + [filteredPrice,actualTime]=fasttimefilter(price,time,filteredTime); + otherwise + error('Unrecogniced SAMPLINGTYPE.') +end + +% Finally convert filteredTime back to the original time format +if strcmp(timeType,'wall') + filteredTime = unit2wall(filteredTime,time0,time1); + actualTime = unit2wall(actualTime,time0,time1); +elseif strcmp(timeType,'seconds') + filteredTime = unit2seconds(filteredTime,time0,time1); + actualTime = unit2seconds(actualTime,time0,time1); +end + + + +function [filteredPrice,actualTime]=fasttimefilter(price,time,filteredTime) + +% Get the size of the inputs +m=size(price,1); +n=size(filteredTime,1); +% This uses a 2-index algorithm so that it is fast for any realistic size. +timeIndex=1; +filteredTimeIndex=1; +% Pl hold the index values. Initializing to 1 makes the back fill easy +pl=ones(n,1); +while timeIndex<=m && filteredTimeIndex<=n + if time(timeIndex)<=filteredTime(filteredTimeIndex) + pl(filteredTimeIndex)=timeIndex; + timeIndex=timeIndex+1; + elseif filteredTimeIndex=time(timeIndex) + while filteredTimeIndexfilteredTime(n) + % No more to assign, so break + break + end +end + +% Clean up any trailing ones +starter = find(diff(pl)<0) + 1; +if ~isempty(starter) + pl(starter:length(pl)) = pl(starter-1); +end +% Use pl the index the filteredPrice and filterTimeActual +filteredPrice = price(pl); +actualTime = time(pl); + diff --git a/realized/realized_qmle_variance.m b/realized/realized_qmle_variance.m new file mode 100644 index 0000000..ded6156 --- /dev/null +++ b/realized/realized_qmle_variance.m @@ -0,0 +1,233 @@ +function [rqv,diagnostics]=realized_qmle_variance(price,time,timeType,samplingType,samplingInterval,options) +% Estimated quadratic variation using QMLE +% +% USAGE: +% [RQV] = realized_qmle_variance(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL) +% [RQV,DIAGNOSTICS] = realized_qmle_variance(PRICE,TIME,TIMETYPE,SAMPLINGTYPE,SAMPLINGINTERVAL,OPTIONS) +% +% INPUTS: +% PRICE - m by 1 vector of high frequency prices +% TIME - [OPTIONAL] m by 1 vector of times where TIME(i) corresponds to PRICE(i). +% TIMETYPE - [OPTIONAL] String describing the way times are measured +% 'wall' 24-hour clock of the form HHMMSS.mmm, e.g. 101543 or 153217 +% 'seconds' Time measured in seconds past midnight +% 'unit' Unit normalized date format, e.g. .1, .234, .9 +% Unit normalized times are more general than the other types and can be +% applied to data from more than one calendar day +% SAMPLINGTYPE - [OPTIONAL] String describing the type of sampling to use when +% filtering PRICE +% 'CalendarTime' - Sample in calendar time using observations separated by +% SAMPLINGINTERVAL seconds +% 'CalendarUniform' - Sample in calendar time using SAMPLINGINTERVAL +% observations spread uniformly between TIME(1) and TIME(m) +% 'BusinessTime' - Sample in business (tick) time using observation separated +% by SAMPLINGINTERVAL ticks +% 'BusinessUniform' - Sample in business (tick) time using observations +% uniformly spaced in business time. +% 'Fixed' - Sample at specific points in time. When using fixed, +% SAMPLINGINTERVAL must be a n by 1 vector of times with the same TIMETYPE +% as TIME (i.e. seconds if TIME is in seconds) +% SAMPLINGINTERVAL - [OPTIONAL] Scalar integer or n by 1 vector whose meaning depends on the +% selected SAMPLINGTYPE +% OPTIONS - [OPTIONAL] Realized option structure initialized by calling +% realized_options('QMLE'). See help realized_options for a description of +% available options. +% +% OUTPUTS: +% RQV - Realized variace estimate as computed by QMLE +% DIAGNOSTICS - Structure of useful diagnostic information. Fields are +% NOISEVARIANCE - Estimated noise variance as computed using QMLE +% ITERATIONS - Number of iterations needed to converge +% +% COMMENTS: +% +% EXAMPLES: +% % Realized QMLE variance using all data +% rqv = realized_qmle_variance(price) +% % Realized QMLE variance using every 10 observations, to avoid dependence in the MMN +% rqv = realized_qmle_variance(price,[],[],'BusinessTime',10) + +% Copyright: Kevin Sheppard +% kevin.sheppard@economics.ox.ac.uk +% Revision: 3 Date: 3/10/2011 + +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +switch nargin + case 1 + time=[]; + timeType=[]; + samplingType=[]; + samplingInterval=[]; + options=[]; + case 2 + timeType=[]; + samplingType=[]; + samplingInterval=[]; + options=[]; + case 3 + samplingType=[]; + samplingInterval=[]; + options=[]; + case 4 + samplingInterval=[]; + options=[]; + case 5 + options=[]; + case 6 + % Nothing + otherwise + error('One to six inputs required.') +end + +if isempty(timeType) && ~isempty(time) + error('TIMETYPE must be provided if TIME is user supplied.') +end + +if isempty(time) + time = (1:length(price))'/price; +end + +if isempty(timeType) + timeType = 'unit'; +end + +if isempty(samplingType) + timeType = 'BusinessTime'; +end +if isempty(samplingInterval) + samplingInterval = 1; +end + +if size(price,2)>size(price,1) + price=price'; +end +if size(price,2)>1 + error('PRICE must be a m by 1 vector.') +end +if size(time,2)>size(time,1) + time=time'; +end +if any(diff(time)<0) + error('TIME must be sorted and increasing') +end +if size(time,2)>1 || length(time)~=length(price) + error('TIME must be a m by 1 vector.') +end +% Inserted to protect against inputing integer times +time = double(time); + +timeType=lower(timeType); +if ~ismember(timeType,{'wall','seconds','unit'}) + error('TIMETYPE must be one of ''wall'', ''seconds'' or ''unit''.'); +end +samplingType=lower(samplingType); +if ~ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform','fixed'}) + error('SAMPLINGTYPE must be one of ''CalendarTime'', ''CalendarUniform'', ''BusinessTime'', ''BusinessUniform'' or ''Fixed''.'); +end + +m=size(price,1); +t0=time(1); +tT=time(m); +if ismember(samplingType,{'calendartime','calendaruniform','businesstime','businessuniform'}) + % Must be a scalar integer if timeType is seconds or wall + if ismember(timeType,{'wall','seconds'}) + if ~isscalar(samplingInterval) || floor(samplingInterval)~=samplingInterval || samplingInterval<1 + error('SAMPLINGINTERVAL must be a positive integer for the SAMPLINGTYPE selected when using ''wall'' or ''seconds'' as TIMETYPE.') + end + else + if ~isscalar(samplingInterval) || samplingInterval<0 + error('SAMPLINGINTERVAL must be a positive value for the SAMPLINGTYPE selected when using ''unit'' as TIMETYPE.') + end + end +else + if size(samplingInterval,2)>size(samplingInterval,1) + samplingInterval=samplingInterval'; + end + if ~(any(samplingInterval>=t0) && any(samplingInterval<=tT)) + error('At least one sampling interval must be between min(TIME) and max(TIME) when using ''Fixed'' as SAMPLINGTYPE.') + end + if any(diff(samplingInterval)<=0) + error('When using ''Fixed'' as SAMPLINGTYPE the vector of sampling times in SAMPLINGINTERVAL must be sorted and strictly increasing.') + end +end + +if nargin==6 && ~isempty(subsamples) + if ~isscalar(subsamples) || subsamples<0 || floor(subsamples)~=subsamples + error('SUBSAMPLES must be a non-negative scalar.') + end +end + +if nargin<7 || isempty(options) + options = realized_options('QMLE'); +end +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Input Checking +%%%%%%%%%%%%%%%%%%%%%%%%%%%% +logPrice = log(price); +[filteredLogPrice,filteredTimes] = realized_price_filter(logPrice,time,timeType,samplingType,samplingInterval); +% Need starting values for sigma2 and omega2 +noisePrice = realized_price_filter(logPrice,time,timeType,options.noiseVarianceSamplingType,options.noiseVarianceSamplingInterval); +noiseReturn = diff(noisePrice); +omega2 = noiseReturn'*noiseReturn/length(noiseReturn); + +r = diff(filteredLogPrice); +n = size(r,1); +sigma2 = realized_variance(logPrice,time,timeType,options.medFrequencySamplingType,options.medFrequencySamplingInterval); +delta = 1/n; +L = spalloc(n,n,4+3*(n-2)); +diagInd = (0:n-1)*n+(1:n); +uDiagInd = (1:n-1)*n+(1:n-1); +lDiagInd = (0:n-2)*n+(2:n); +L(diagInd)=2; +L(uDiagInd)=-1; +L(lDiagInd)=-1; +O = spalloc(n,n,4+3*(n-2)); + +theta = [sigma2;omega2]; +thetaOld = [-1;-1]; +iter = 0; +while max(abs(theta-thetaOld)>1e-3) && iter<20 + thetaOld = theta; + O(diagInd) = sigma2 * delta + 2*omega2; + O(lDiagInd) = -omega2; + O(uDiagInd) = -omega2; + Om1 = inv(O); + Om1 = (Om1+Om1')/2; + Om2= inv(O*O); + Om2 = (Om2+Om2')/2; + Om1L = Om1*L; + Om2L = Om2*L; + Om2L2 = Om2L*L; + Om1LOm1 = Om1L*Om1; + Om1LOm1 = (Om1LOm1+Om1LOm1')/2; + + trOm2L = diag(Om2L)'*ones(n,1); + trOm2L2 = diag(Om2L2)'*ones(n,1); + trOm2 = diag(Om2)'*ones(n,1); + denom = (trOm2L)^2 - (trOm2) * (trOm2L2); + W1 = n * trOm2L * Om1LOm1 - n * trOm2L2 * Om2; + W1 = W1 / denom; + W1 = (W1+W1')/2; + W2 = trOm2L * Om2 - trOm2 * Om1LOm1; + W2 = W2/denom; + W2 = (W2+W2')/2; + + sigma2 = r'*W1*r; + omega2 = r'*W2*r; + omega2 = max(0,omega2); + theta = [sigma2;omega2]; + iter = iter + 1; + disp(iter) + disp(theta) +end + +if max(abs(theta-thetaOld)>1e-3) && iter>=20 + warning('MFE::Convergence','The realized QMLE estimator did not converge.'); +end + + +rqv = sigma2; +diagnostics.iterations = iter; +diagnostics.noiseVariance = omega2; \ No newline at end of file diff --git a/realized/realized_quantile_scales.mat b/realized/realized_quantile_scales.mat new file mode 100644 index 0000000000000000000000000000000000000000..8581fd9581df8886ed516756e734c2924a2a55b3 GIT binary patch literal 549815 zcmb4o1y>wR6K)8>AvgqryK4x(iw1|_ZXtMZ*Tpqx&;)k~7Tn!!aS84aWbp-d7cTF2 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