List of included code files

A full list of Matlab code files, organized loosely into broad categories, with brief descriptions

Introduction

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 run with multiple input parameters, with each parameter set yielding characteristic outputs. For example,

• 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; and

• 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.

Distribution

Algorithms for summarizing properties of the distribution of values in a time series (independent of their ordered 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 the histogram.
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	Fits of parametric distributions or simple time-series models.
DN_Spread	Spread of the input time series.
DN_TrimmedMean	Mean of the outlier-trimmed time series.
DN_HistogramAsymmetry	Distributional asymmetry.
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.

Correlation

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_FirstCrossing	First time the autocorrelation function crosses a threshold.
CO_FirstMin	Time of first minimum in a given correlation 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.

Information Theory

Entropy and complexity measures for time series based on information theory

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 section 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.
NL_nsamdf	Nonlinearity measure derived from the nonlinear average magnitude difference function.
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.

Others

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.