fs_movingaverage.m

%% Matlab Moving Average of Time-series 
% *back to* <https://fanwangecon.github.io *Fan*>*'s* <https://fanwangecon.github.io/Math4Econ/ 
% *Intro Math for Econ*>*,*  <https://fanwangecon.github.io/M4Econ/ *Matlab Examples*>*, 
% or* <https://fanwangecon.github.io/MEconTools/ *MEconTools*> *Repositories*
%% Weighted Average of Neighbors
% Not actually a time-series moving average. There is a vector of a parameter 
% value, this parameter is not been estimated, we estimate all other parameters 
% while varying this one parameter. At different values of this parameter, there 
% is a vector of estimates. We have estimated a model along a equi-distance grid 
% of this exogenous parameter. Now for each of the estimated parameter, calculate 
% a "moving-average" based on averaging across estimated neighbor values of this 
% parameter, where neighbor distance is defined by the fixed exogenous parameter. 
% Why do this? This can be considered a "smoother" tool, but more importantly, 
% use the moving averages as new initial parameter guesses for a new round of 
% estimation at each of the exogenous parameter's values. For different starting 
% seeds, use different moving windows.
% 
% First, select out all estimates:

% Load in file
srn_excel_exa = 'C:\Users\fan\M4Econ\table\_exa\excel_exa.xlsx';
tb_estimates = readtable(srn_excel_exa);
% columns to select
ar_st_colnames = tb_estimates.Properties.VariableNames;
ar_st_colnames_sel = ["mean_h_sd", ar_st_colnames(endsWith(ar_st_colnames, '_esti'))];
% Select all estimates columns and the exogenous parameter column
mt_estimates_sel = tb_estimates{:, ar_st_colnames_sel};
% sort by the first column
mt_estimates_sel = sortrows(mt_estimates_sel, 1);
disp(mt_estimates_sel(1:10,:));
% show size
disp(size(mt_estimates_sel));
%% 
% Second, calculate moving aveage with <https://www.mathworks.com/help/matlab/ref/movmean.html#bu6jxup 
% movmean>, take the mean of up to 33 surrounding values, 66 and 99. Note that 
% there is only 82 elements of the array. But the movmean function's window parameter 
% will divide the window left and right.

mt_estimates_mov33 = movmean(mt_estimates_sel, 33);
mt_estimates_mov66 = movmean(mt_estimates_sel, 66);
mt_estimates_movflat = movmean(mt_estimates_sel, size(mt_estimates_sel,1)*2);
%% 
% Visualize using the <https://fanwangecon.github.io/MEconTools/MEconTools/doc/graph/htmlpdfm/fx_graph_grid.html 
% ff_graph_grid> function from <https://fanwangecon.github.io/MEconTools/ MEconTools> 
% moving average for one parameter, with different windows. Note that with a moving 
% window of 82*2, the moving average becomes flat, because there are 82 elements 
% of the underlying "time-series", so the window needs to be 82*2 for the moving 
% average to be fully flat.

% Generate some Data
ar_row_grid = ["actual", "moving avg widow=33","mov window=66","mov window=82*2"];
ar_exo_param_grid = mt_estimates_sel(:, 1);
it_col = 4;
mt_mov_value = [mt_estimates_sel(:,it_col), ...
    mt_estimates_mov33(:,it_col), ...
    mt_estimates_mov66(:,it_col), ...
    mt_estimates_movflat(:,it_col)]'; 
% container map settings
mp_support_graph = containers.Map('KeyType', 'char', 'ValueType', 'any');
mp_support_graph('cl_st_graph_title') = {'Moving Average with Widening Sliding Windows'};
mp_support_graph('cl_st_ytitle') = {'Parameter Estimates Moving Average'};
mp_support_graph('cl_st_xtitle') = {'Exogenous Parameter (not estimated)'};
mp_support_graph('st_legend_loc') = 'best';
mp_support_graph('bl_graph_logy') = false;
mp_support_graph('it_legend_select') = 4; % how many shock legends to show
mp_support_graph('st_rounding') = '6.2f'; % format shock legend
mp_support_graph('cl_scatter_shapes') = {'s', 'o', '*', 'x'};
mp_support_graph('cl_colors') = 'lines';
% Call function
ff_graph_grid(mt_mov_value, ar_row_grid, ar_exo_param_grid, mp_support_graph);