Highly comparative time-series analysis using h...

List of included code files

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.
Distribution
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.
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_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.
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.

Introduction

Example analysis code

Last updated 3 years ago

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.

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.

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.

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.

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 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.

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.

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.

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.

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.

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.