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List of code files used in hctsa

Here we provide a full list of Matlab code files, organized loosely into broad categories, and with brief descriptions.

The full default set of over 7700 features in hctsa is produced by running all of the code files below, many of which produce a large number of outputs (e.g., some functions fit a time-series model and then output statistics including the parameters of the best-fitting model, measures of the model's goodness of fit, the optimal model order, and autocorrelation statistics on the residuals). In our default feature set, each function is also run with different sets of input parameters, with each parameter set yielding characteristic outputs. For example, different inputs to CO_AutoCorr determine the method in which autocorrelation is computed, as well as the time lag at which autocorrelation is calculated, e.g., lag 1, lag 2, lag 3, etc.; WL_dwtcoeff has inputs that set the mother wavelet to use, and level of wavelet decomposition; FC_LocalSimple has inputs that determine the time-series forecasting method to use and the size of the training window. The set of code files below and their input parameters that define the default hctsa feature set are in the INP_mops.txt file of the hctsa repository.


Code summarizing properties of the distribution of values in a time series (disregarding their sequence through time).

Code file Description
DN_Burstiness Burstiness statistic of a time series.
DN_CompareKSFit Fits a distribution to data.
DN_CustomSkewness Custom skewness measures.
DN_FitKernelSmooth Statistics of a kernel-smoothed distribution of the data.
DN_Fit_mle Maximum likelihood distribution fit to data.
DN_HighLowMu The highlowmu statistic.
DN_HistogramMode Mode of a data vector.
DN_Mean A given measure of location of a data vector.
DN_MinMax The maximum and minimum values of the input data vector
DN_Moments A moment of the distribution of the input time series.
DN_OutlierInclude How statistics depend on distributional outliers.
DN_OutlierTest How distributional statistics depend on distributional outliers.
DN_ProportionValues Proportion of values in a time-series vector.
DN_Quantile Quantiles of the distribution of values in the time series data vector.
DN_RemovePoints How time-series properties change as points are removed.
DN_SimpleFit Fit distributions or simple time-series models to the data.
DN_Spread Measure of spread of the input time series.
DN_TrimmedMean Mean of the trimmed time series using trimmean.
DN_Unique The proportion of the time series that are unique values.
DN_Withinp Proportion of data points within p standard deviations of the mean.
DN_cv Coefficient of variation.
DN_pleft Distance from the mean at which a given proportion of data are more distant.
EN_DistributionEntropy Distributional entropy.
HT_DistributionTest Hypothesis test for distributional fits to a data vector.


Code summarizing basic properties of how values of a time series are correlated through time.

Code file Description
CO_AddNoise Changes in the automutual information with the addition of noise.
CO_AutoCorr Compute the autocorrelation of an input time series.
CO_AutoCorrShape How the autocorrelation function changes with the time lag.
CO_Embed2 Statistics of the time series in a 2-dimensional embedding space.
CO_Embed2_AngleTau Angle autocorrelation in a 2-dimensional embedding space.
CO_Embed2_Basic Point density statistics in a 2-d embedding space.
CO_Embed2_Dist Analyzes distances in a 2-d embedding space of a time series.
CO_Embed2_Shapes Shape-based statistics in a 2-d embedding space.
CO_FirstMin Time of first minimum in a given correlation function.
CO_FirstZero The first zero-crossing of a given autocorrelation function.
CO_NonlinearAutocorr A custom nonlinear autocorrelation of a time series.
CO_StickAngles Analysis of line-of-sight angles between time-series data points.
CO_TranslateShape Statistics on datapoints inside geometric shapes across the time series.
CO_f1ecac The 1/e correlation length.
CO_fzcglscf The first zero-crossing of the generalized self-correlation function.
CO_glscf The generalized linear self-correlation function of a time series.
CO_tc3 Normalized nonlinear autocorrelation function, tc3.
CO_trev Normalized nonlinear autocorrelation, trev function of a time series.
DK_crinkle Computes James Theiler's crinkle statistic.
DK_theilerQ Computes Theiler's Q statistic.
DK_timerev Time reversal asymmetry statistic.
NL_embed_PCA Principal Components analysis of a time series in an embedding space.
Automutual information:
CO_RM_AMInformation Automutual information (Rudy Moddemeijer implementation).
CO_CompareMinAMI Variability in first minimum of automutual information.
CO_HistogramAMI The automutual information of the distribution using histograms.
IN_AutoMutualInfoStats Statistics on automutual information function for a time series.

Entropy and information theory

Entropy and complexity measures for time series

Code file Description
EN_ApEn Approximate Entropy of a time series.
EN_CID Simple complexity measure of a time series.
EN_MS_LZcomplexity Lempel-Ziv complexity of a n-bit encoding of a time series.
EN_MS_shannon Approximate Shannon entropy of a time series.
EN_PermEn Permutation Entropy of a time series.
EN_RM_entropy Entropy of a time series using Rudy Moddemeijer's code.
EN_Randomize How time-series properties change with increasing randomization.
EN_SampEn Sample Entropy of a time series.
EN_mse Multiscale entropy of a time series.
EN_rpde Recurrence period density entropy (RPDE).
EN_wentropy Entropy of time series using wavelets.

Time-series model fitting and forecasting

Fitting time-series models, and doing simple forecasting on time series.

Code file Description
MF_ARMA_orders Compares a range of ARMA models fitted to a time series.
MF_AR_arcov Fits an AR model of a given order, p.
MF_CompareAR Compares model fits of various orders to a time series.
MF_CompareTestSets Robustness of test-set goodness of fit.
MF_ExpSmoothing Exponential smoothing time-series prediction model.
MF_FitSubsegments Robustness of model parameters across different segments of a time series.
MF_GARCHcompare Comparison of GARCH time-series models.
MF_GARCHfit GARCH time-series modeling.
MF_GP_FitAcross Gaussian Process time-series modeling for local prediction.
MF_GP_LocalPrediction Gaussian Process time-series model for local prediction.
MF_GP_hyperparameters Gaussian Process time-series model parameters and goodness of fit.
MF_StateSpaceCompOrder Change in goodness of fit across different state space models.
MF_StateSpace_n4sid State space time-series model fitting.
MF_arfit Statistics of a fitted AR model to a time series.
MF_armax Statistics on a fitted ARMA model.
MF_hmm_CompareNStates Hidden Markov Model (HMM) fitting to a time series.
MF_hmm_fit Fits a Hidden Markov Model to sequential data.
MF_steps_ahead Goodness of model predictions across prediction lengths.
FC_LocalSimple Simple local time-series forecasting.
FC_LoopLocalSimple How simple local forecasting depends on window length.
FC_Surprise How surprised you would be of the next data point given recent memory.
PP_ModelFit Investigates whether AR model fit improves with different preprocessings.

Stationarity and step detection

Quantifying how properties of a time series change over time.

Code file Description
SY_DriftingMean Mean and variance in local time-series subsegments.
SY_DynWin How stationarity estimates depend on the number of time-series subsegments.
SY_KPSStest The KPSS stationarity test.
SY_LocalDistributions Compares the distribution in consecutive time-series segments.
SY_LocalGlobal Compares local statistics to global statistics of a time series.
SY_PPtest Phillips-Peron unit root test.
SY_RangeEvolve How the time-series range changes across time.
SY_SlidingWindow Sliding window measures of stationarity.
SY_SpreadRandomLocal Bootstrap-based stationarity measure.
SY_StatAv Simple mean-stationarity metric, StatAv.
SY_StdNthDer Standard deviation of the nth derivative of the time series.
SY_StdNthDerChange How the output of SY_StdNthDer changes with order parameter.
SY_TISEAN_nstat_z Cross-forecast errors of zeroth-order time-series models.
SY_VarRatioTest Variance ratio test for random walk.
Step detection:
CP_ML_StepDetect Analysis of discrete steps in a time series.
CP_l1pwc_sweep_lambda Dependence of step detection on regularization parameter.
CP_wavelet_varchg Variance change points in a time series.

Nonlinear time-series analysis and fractal scaling

Nonlinear time-series analysis methods, including embedding dimensions and fluctuation analysis.

Code file Description
NL_BoxCorrDim Correlation dimension of a time series.
NL_DVV Delay Vector Variance method for real and complex signals.
NL_MS_fnn False nearest neighbors of a time series.
NL_MS_nlpe Normalized drop-one-out constant interpolation nonlinear prediction error.
NL_TISEAN_c1 Information dimension.
NL_TISEAN_d2 d2 routine from the TISEAN package.
NL_TISEAN_fnn False nearest neighbors of a time series.
NL_TSTL_FractalDimensions Fractal dimension spectrum, D(q), of a time series.
NL_TSTL_GPCorrSum Correlation sum scaling by Grassberger-Proccacia algorithm.
NL_TSTL_LargestLyap Largest Lyapunov exponent of a time series.
NL_TSTL_PoincareSection Poincare sectino analysis of a time series.
NL_TSTL_ReturnTime Analysis of the histogram of return times.
NL_TSTL_TakensEstimator Taken's estimator for correlation dimension.
NL_TSTL_acp acp function in TSTOOL
NL_TSTL_dimensions Box counting, information, and correlation dimension of a time series.
NL_crptool_fnn Analyzes the false-nearest neighbors statistic.
SD_SurrogateTest Analyzes test statistics obtained from surrogate time series.
SD_TSTL_surrogates Surrogate time-series analysis.
TSTL_delaytime Optimal delay time using the method of Parlitz and Wichard.
TSTL_localdensity Local density estimates in the time-delay embedding space.
Fluctuation analysis:
SC_MMA Physionet implementation of multiscale multifractal analysis
SC_fastdfa Matlab wrapper for Max Little's ML_fastdfa code
SC_FluctAnal Implements fluctuation analysis by a variety of methods.

Fourier and wavelet transforms, periodicity measures

Properties of the time-series power spectrum, wavelet spectrum, and other periodicity measures.

Code file Description
SP_Summaries Statistics of the power spectrum of a time series.
DT_IsSeasonal A simple test of seasonality.
PD_PeriodicityWang Periodicity extraction measure of Wang et al.
WL_DetailCoeffs Detail coefficients of a wavelet decomposition.
WL_coeffs Wavelet decomposition of the time series.
WL_cwt Continuous wavelet transform of a time series.
WL_dwtcoeff Discrete wavelet transform coefficients.
WL_fBM Parameters of fractional Gaussian noise/Brownian motion in a time series.
WL_scal2frq Frequency components in a periodic time series.

Symbolic transformations

Properties of a discrete symbolization of a time series.

Code file Description
SB_BinaryStats Statistics on a binary symbolization of the time series.
SB_BinaryStretch Characterizes stretches of 0/1 in time-series binarization.
SB_MotifThree Motifs in a coarse-graining of a time series to a 3-letter alphabet.
SB_MotifTwo Local motifs in a binary symbolization of the time series.
SB_TransitionMatrix Transition probabilities between different time-series states.
SB_TransitionpAlphabet How transition probabilities change with alphabet size.

Statistics from biomedical signal processing

Simple time-series properties derived mostly from the heart rate variability (HRV) literature.

Code file Description
MD_hrv_classic Classic heart rate variability (HRV) statistics.
MD_pNN pNNx measures of heart rate variability.
MD_polvar The POLVARd measure of a time series.
MD_rawHRVmeas Heart rate variability (HRV) measures of a time series.

Basic statistics, trend

Basic statistics of a time series, including measures of trend.

Code file Description
SY_Trend Quantifies various measures of trend in a time series.
ST_FitPolynomial Goodness of a polynomial fit to a time series.
ST_Length Length of an input data vector.
ST_LocalExtrema How local maximums and minimums vary across the time series.
ST_MomentCorr Correlations between simple statistics in local windows of a time series.
ST_SimpleStats Basic statistics about an input time series.


Other properties, like extreme values, visibility graphs, physics-based simulations, and dependence on pre-processings applied to a time series.

Code file Description
EX_MovingThreshold Moving threshold model for extreme events in a time series.
HT_HypothesisTest Statistical hypothesis test applied to a time series.
NW_VisibilityGraph Visibility graph analysis of a time series.
PH_ForcePotential Couples the values of the time series to a dynamical system.
PH_Walker Simulates a hypothetical walker moving through the time domain.
PP_Compare Compare how time-series properties change after pre-processing.
PP_Iterate How time-series properties change in response to iterative pre-processing.