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_AutoCorrdetermine 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_dwtcoeffhas inputs that set the mother wavelet to use and level of wavelet decomposition; andFC_LocalSimplehas 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_BurstinessBurstiness statistic of a time series.
DN_CompareKSFitFits a distribution to data.
DN_CustomSkewnessCustom skewness measures.
DN_FitKernelSmoothStatistics of a kernel-smoothed distribution of the data.
DN_Fit_mleMaximum likelihood distribution fit to data.
DN_HighLowMuThe highlowmu statistic.
DN_HistogramModeMode of the histogram.
DN_MeanA given measure of location of a data vector.
DN_MinMaxThe maximum and minimum values of the input data vector
DN_MomentsA moment of the distribution of the input time series.
DN_OutlierIncludeHow statistics depend on distributional outliers.
DN_OutlierTestHow distributional statistics depend on distributional outliers.
DN_ProportionValuesProportion of values in a time-series vector.
DN_QuantileQuantiles of the distribution of values in the time series data vector.
DN_RemovePointsHow time-series properties change as points are removed.
DN_SimpleFitFits of parametric distributions or simple time-series models.
DN_SpreadSpread of the input time series.
DN_TrimmedMeanMean of the outlier-trimmed time series.
DN_HistogramAsymmetryDistributional asymmetry.
DN_UniqueThe proportion of the time series that are unique values.
DN_WithinpProportion of data points within p standard deviations of the mean.
DN_cvCoefficient of variation.
DN_pleftDistance from the mean at which a given proportion of data are more distant.
EN_DistributionEntropyDistributional entropy.
HT_DistributionTestHypothesis 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_AddNoiseChanges in the automutual information with the addition of noise.
CO_AutoCorrCompute the autocorrelation of an input time series.
CO_AutoCorrShapeHow the autocorrelation function changes with the time lag.
CO_Embed2Statistics of the time series in a 2-dimensional embedding space.
CO_Embed2_AngleTauAngle autocorrelation in a 2-dimensional embedding space.
CO_Embed2_BasicPoint density statistics in a 2-d embedding space.
CO_Embed2_DistAnalyzes distances in a 2-d embedding space of a time series.
CO_Embed2_ShapesShape-based statistics in a 2-d embedding space.
CO_FirstCrossingFirst time the autocorrelation function crosses a threshold.
CO_FirstMinTime of first minimum in a given correlation function.
CO_NonlinearAutocorrA custom nonlinear autocorrelation of a time series.
CO_StickAnglesAnalysis of line-of-sight angles between time-series data points.
CO_TranslateShapeStatistics on datapoints inside geometric shapes across the time series.
CO_f1ecacThe 1/e correlation length.
CO_fzcglscfThe first zero-crossing of the generalized self-correlation function.
CO_glscfThe generalized linear self-correlation function of a time series.
CO_tc3Normalized nonlinear autocorrelation function,
tc3.CO_trevNormalized nonlinear autocorrelation,
trev function of a time series.DK_crinkleComputes James Theiler's crinkle statistic.
DK_theilerQComputes Theiler's Q statistic.
DK_timerevTime reversal asymmetry statistic.
NL_embed_PCAPrincipal Components analysis of a time series in an embedding space.
Automutual information:
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CO_RM_AMInformationAutomutual information (Rudy Moddemeijer implementation).
CO_CompareMinAMIVariability in first minimum of automutual information.
CO_HistogramAMIThe automutual information of the distribution using histograms.
IN_AutoMutualInfoStatsStatistics 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_ApEnApproximate Entropy of a time series.
EN_CIDSimple complexity measure of a time series.
EN_MS_LZcomplexityLempel-Ziv complexity of a n-bit encoding of a time series.
EN_MS_shannonApproximate Shannon entropy of a time series.
EN_PermEnPermutation Entropy of a time series.
EN_RM_entropyEntropy of a time series using Rudy Moddemeijer's code.
EN_RandomizeHow time-series properties change with increasing randomization.
EN_SampEnSample Entropy of a time series.
EN_mseMultiscale entropy of a time series.
EN_rpdeRecurrence period density entropy (RPDE).
EN_wentropyEntropy 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_ordersCompares a range of ARMA models fitted to a time series.
MF_AR_arcovFits an AR model of a given order, p.
MF_CompareARCompares model fits of various orders to a time series.
MF_CompareTestSetsRobustness of test-set goodness of fit.
MF_ExpSmoothingExponential smoothing time-series prediction model.
MF_FitSubsegmentsRobustness of model parameters across different segments of a time series.
MF_GARCHcompareComparison of GARCH time-series models.
MF_GARCHfitGARCH time-series modeling.
MF_GP_FitAcrossGaussian Process time-series modeling for local prediction.
MF_GP_LocalPredictionGaussian Process time-series model for local prediction.
MF_GP_hyperparametersGaussian Process time-series model parameters and goodness of fit.
MF_StateSpaceCompOrderChange in goodness of fit across different state space models.
MF_StateSpace_n4sidState space time-series model fitting.
MF_arfitStatistics of a fitted AR model to a time series.
MF_armaxStatistics on a fitted ARMA model.
MF_hmm_CompareNStatesHidden Markov Model (HMM) fitting to a time series.
MF_hmm_fitFits a Hidden Markov Model to sequential data.
MF_steps_aheadGoodness of model predictions across prediction lengths.
FC_LocalSimpleSimple local time-series forecasting.
FC_LoopLocalSimpleHow simple local forecasting depends on window length.
FC_SurpriseHow surprised you would be of the next data point given recent memory.
PP_ModelFitInvestigates 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_DriftingMeanMean and variance in local time-series subsegments.
SY_DynWinHow stationarity estimates depend on the number of time-series subsegments.
SY_KPSStestThe KPSS stationarity test.
SY_LocalDistributionsCompares the distribution in consecutive time-series segments.
SY_LocalGlobalCompares local statistics to global statistics of a time series.
SY_PPtestPhillips-Peron unit root test.
SY_RangeEvolveHow the time-series range changes across time.
SY_SlidingWindowSliding window measures of stationarity.
SY_SpreadRandomLocalBootstrap-based stationarity measure.
SY_StatAvSimple mean-stationarity metric,
StatAv.SY_StdNthDerStandard deviation of the nth derivative of the time series.
SY_StdNthDerChangeHow the output of
SY_StdNthDer changes with order parameter.SY_TISEAN_nstat_zCross-forecast errors of zeroth-order time-series models.
SY_VarRatioTestVariance ratio test for random walk.
Step detection:
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CP_ML_StepDetectAnalysis of discrete steps in a time series.
CP_l1pwc_sweep_lambdaDependence of step detection on regularization parameter.
CP_wavelet_varchgVariance 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_BoxCorrDimCorrelation dimension of a time series.
NL_DVVDelay Vector Variance method for real and complex signals.
NL_MS_fnnFalse nearest neighbors of a time series.
NL_MS_nlpeNormalized drop-one-out constant interpolation nonlinear prediction error.
NL_TISEAN_c1Information dimension.
NL_TISEAN_d2d2 routine from the TISEAN package.NL_TISEAN_fnnFalse nearest neighbors of a time series.
NL_TSTL_FractalDimensionsFractal dimension spectrum,
D(q), of a time series.NL_TSTL_GPCorrSumCorrelation sum scaling by Grassberger-Proccacia algorithm.
NL_TSTL_LargestLyapLargest Lyapunov exponent of a time series.
NL_TSTL_PoincareSectionPoincare section analysis of a time series.
NL_TSTL_ReturnTimeAnalysis of the histogram of return times.
NL_TSTL_TakensEstimatorTaken's estimator for correlation dimension.
NL_TSTL_acpacp function in TSTOOLNL_TSTL_dimensionsBox counting, information, and correlation dimension of a time series.
NL_crptool_fnnAnalyzes the false-nearest neighbors statistic.
SD_SurrogateTestAnalyzes test statistics obtained from surrogate time series.
SD_TSTL_surrogatesSurrogate time-series analysis.
TSTL_delaytimeOptimal delay time using the method of Parlitz and Wichard.
TSTL_localdensityLocal density estimates in the time-delay embedding space.
NL_nsamdfNonlinearity measure derived from the nonlinear average magnitude difference function.
Fluctuation analysis:
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SC_MMAPhysionet implementation of multiscale multifractal analysis
SC_fastdfaMatlab wrapper for Max Little's
ML_fastdfa codeSC_FluctAnalImplements 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_SummariesStatistics of the power spectrum of a time series.
DT_IsSeasonalA simple test of seasonality.
PD_PeriodicityWangPeriodicity extraction measure of Wang et al.
WL_DetailCoeffsDetail coefficients of a wavelet decomposition.
WL_coeffsWavelet decomposition of the time series.
WL_cwtContinuous wavelet transform of a time series.
WL_dwtcoeffDiscrete wavelet transform coefficients.
WL_fBMParameters of fractional Gaussian noise/Brownian motion in a time series.
WL_scal2frqFrequency components in a periodic time series.
Symbolic transformations
Properties of a discrete symbolization of a time series.
Code file
Description
SB_BinaryStatsStatistics on a binary symbolization of the time series.
SB_BinaryStretchCharacterizes stretches of 0/1 in time-series binarization.
SB_MotifThreeMotifs in a coarse-graining of a time series to a 3-letter alphabet.
SB_MotifTwoLocal motifs in a binary symbolization of the time series.
SB_TransitionMatrixTransition probabilities between different time-series states.
SB_TransitionpAlphabetHow 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_classicClassic heart rate variability (HRV) statistics.
MD_pNNpNNx measures of heart rate variability.MD_polvarThe
POLVARd measure of a time series.MD_rawHRVmeasHeart 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_TrendQuantifies various measures of trend in a time series.
ST_FitPolynomialGoodness of a polynomial fit to a time series.
ST_LengthLength of an input data vector.
ST_LocalExtremaHow local maximums and minimums vary across the time series.
ST_MomentCorrCorrelations between simple statistics in local windows of a time series.
ST_SimpleStatsBasic 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_MovingThresholdMoving threshold model for extreme events in a time series.
HT_HypothesisTestStatistical hypothesis test applied to a time series.
NW_VisibilityGraphVisibility graph analysis of a time series.
PH_ForcePotentialCouples the values of the time series to a dynamical system.
PH_WalkerSimulates a hypothetical walker moving through the time domain.
PP_CompareCompare how time-series properties change after pre-processing.
PP_IterateHow time-series properties change in response to iterative pre-processing.
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Contents
Introduction
Distribution
Correlation
Information Theory
Time-series model fitting and forecasting
Stationarity and step detection
Nonlinear time-series analysis and fractal scaling
Fourier and wavelet transforms, periodicity measures
Symbolic transformations
Statistics from biomedical signal processing
Basic statistics, trend
Others