API Reference¶
Core¶
A configuration-driven feature extraction calculator for time series data. |
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Local process-based distributor using a pathos ProcessPool. |
Utilities¶
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Load predefined datasets for testing and validation. |
Z-score the input data vector. |
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Decorator for a feature function that returns a dict of outputs (one feature per field). |
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The output of |
Shared hctsa helpers¶
Ports of hctsa’s BF_* helper functions, shared by the methods below (the portable random generator and
its seeds, robust fits, explicit histogram bin edges and kernel densities, and the removal of points).
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Portable pseudo-random numbers: a stream fixed by the seed alone (hctsa |
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The integer seed (for |
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Add tiny, reproducible jitter to break exact ties in |
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Remove or saturate a proportion of the points of a time series (hctsa's |
Signed z-statistic of a runs test for randomness about the median (hctsa |
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Statistics of the residuals of a fit, for remaining structure (hctsa |
Theil-Sen robust straight-line fit (hctsa |
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Global least-squares fit of |
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Deterministic least-squares fit of a simple curve to a density (hctsa |
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Mixture of two Gaussians fitted to a binned distribution by EM (hctsa |
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Least-squares fit of a sum of |
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Gaussian kernel density estimate with an explicit bandwidth (hctsa |
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Equal-width histogram bin edges from an explicit bin-count rule (hctsa |
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Histogram bin edges at the quantiles of the data: equiprobable bins (hctsa |
Half-sample mode: a robust, bin-free estimate of the mode (hctsa |
Time-Series Analysis Method Modules¶
Changepoint¶
Analysis of discrete steps in a time series. |
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Dependence of step detection on regularization parameter. |
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Number of variance change points found from a wavelet detail signal. |
Correlation¶
Detects temporal oversampling relative to a series' own dynamics. |
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Kullback-Leibler divergence between forward and time-reversed embeddings. |
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Compute the autocorrelation of an input time series. |
Shape of the time-reversibility profile of a time series. |
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Changes in the automutual information with the addition of noise. |
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Theiler's Q statistic, a third-moment statistic of sums of adjacent samples. |
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Crinkle statistic: normalized fourth moment of the second difference. |
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Time-reversal asymmetry statistic (D. |
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Asymmetry of local dynamics between positive and negative regimes. |
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Angle autocorrelation in a 2-dimensional delay embedding, over delays. |
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Statistics of the time series in a 2-dimensional embedding space. |
Periodicity extraction measure of Wang et al. (2007). |
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Assess the variability in the first minimum of automutual information (AMI) across binning strategies. |
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The automutual information of the distribution using histograms. |
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Analysis of the angles between successive same-sign time-series values. |
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Physical falling-sticks model of line-of-sight interaction. |
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Compute a custom nonlinear autocorrelation of a time series. |
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Compute the partial autocorrelation of an input time series. |
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Analyzes distances in a 2-dimensional embedding space of a time series. |
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Point-density statistics in a two-dimensional delay embedding. |
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Shape-based statistics in a 2-d embedding space. |
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The first zero-crossing of the generalized self-correlation function. |
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Compute the generalized linear self-correlation function (GLSCF) of a time series. |
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The first crossing of a given autocorrelation function across a given threshold. |
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Statistics on datapoints inside geometric shapes across the time series. |
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How the autocorrelation function changes with the time lag. |
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Normalized nonlinear autocorrelation (trev) function of a time series. |
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Normalized nonlinear autocorrelation function, tc3. |
Tests for non-Gaussianity of the joint, time-lagged embedding distribution. |
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How well each subsequence shape recurs elsewhere in a time series (the matrix profile). |
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Serial dependence of the series being below its own quantiles (the quantilogram). |
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How the autocorrelation of a time series changes when a set of points is removed or clipped. |
Criticality¶
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Compute the Rescaled Auto-Density (RAD) feature of a time series. |
Distribution¶
Distributional moments of the input data. |
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Compares a fitted distribution with the smoothed distribution of the data. |
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Proportion of data points within p standard deviations of the mean or median. |
The proportion of the time series that are unique values. |
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Measure of spread of the input time series. |
Calculates the quantile value at a specified proportion, p. |
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Calculate the proportion of values meeting specific conditions in a time series. |
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Distance from the mean at which a given proportion of data are more distant. |
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The maximum and minimum values of the input data vector. |
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A given measure of location of a data vector. |
The high_low_mu statistic. |
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Maximum likelihood distribution fit to data. |
Calculate the coefficient of variation of order k. |
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Compute custom skewness measures of a time series. |
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Calculate burstiness statistics of a time series. |
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A moment of the distribution of the input time series. |
How the timing and spacing of extreme values change as the threshold rises. |
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How distributional statistics depend on distributional outliers. |
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Mean of the trimmed time series. |
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Calculate measures of histogram asymmetry for a time series. |
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Measures the mode of the data vector using histograms with a given number of bins. |
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How time-series properties change as points are removed. |
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Statistics of a kernel-smoothed distribution of the data. |
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Fits a simple curve to the distribution of the values. |
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Tail index of the distribution of values: how heavy its tails are. |
Entropy¶
Approximate Shannon entropy of a time series. |
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Distributional entropy. |
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Multiscale entropy (MSE) of a time series. |
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Compute Sample Entropy (SampEn) of a time series. |
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Permutation Entropy (PermEn) of a time series. |
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Recurrence period density entropy (RPDE). |
Approximate entropy (ApEn) of a time series. |
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Complexity-invariant distance. |
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Compute the normalized Lempel-Ziv (LZ) complexity of an n-bit encoding of a time series. |
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Bubble entropy of a time series. |
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Dispersion entropy of a time series. |
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Fuzzy entropy of a time series. |
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Jensen-Shannon statistical complexity of ordinal patterns. |
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How properties of the series change as it is progressively randomized. |
Wavelet entropy of a time series. |
Extreme Events¶
Moving threshold model for extreme events in a time series. |
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Temporal patterning of positive vs. negative extreme events. |
Graph¶
Visibility graph analysis of a time series. |
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Ordinal partition transition network measures. |
Hypothesis Tests¶
Variance ratio test for random walk. |
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Perform statistical hypothesis testing on a time series. |
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Hypothesis test for distributional fits to a data vector. |
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Statistic or p-value of a test of serial independence. |
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p-value of a hypothesis test about the distribution of values. |
Information¶
Time of first minimum in a given self-correlation function. |
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Time of first maximum in a given self-correlation function. |
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Calculate statistics on the automutual information (AMI) function of a time series. |
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Compute time-delayed automutual information of a time series. |
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Multivariate automutual information, I(x_t; x_{t-tau}, x_{t-2tau}). |
Medical¶
Compute Poincaré plot-based HRV (Heart Rate Variability) measures from RR interval time series. |
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Compute classic heart rate variability (HRV) statistics. |
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Compute the POLVARd measure of a time series. |
Compute pNNx measures of heart rate variability (HRV). |
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Compute Porta's symbolic-dynamics word-type indices. |
Model Fit¶
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A hidden Markov model fitted to the first part of the series, and how well it describes the rest. |
Robustness of model parameters across different segments of a time series. |
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How simple local forecasting depends on window length. |
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Simple local time-series forecasting. |
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Canonical summary of the residuals from a model fit. |
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Exponential smoothing time-series prediction model. |
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Fits an autoregressive (AR) model of a given order p. |
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Statistics of a fitted AR model to a time series. |
Fits a 'sin1' (single frequency sinusoid) model to the time series. |
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Gaussian Process time-series modeling for local prediction. |
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Gaussian Process time-series model for local prediction. |
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How the out-of-sample error of an AR model changes with its order. |
How well a model fitted to the whole series predicts short stretches of it. |
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How well GARCH models of different orders describe the changing variance of the series. |
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A GARCH model of the changing variance of the series, and what it leaves in the residuals. |
Fits a Gaussian process to the series and reports its fitted kernel parameters and goodness of fit. |
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How the fit of a state-space model improves as its order increases. |
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A fitted state-space model of the series, and how well it predicts the later part of the series. |
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The coefficients of a fitted ARMA model, and how well it predicts the later part of the series. |
How the fit of hidden Markov models to the series changes with the number of hidden states. |
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How the accuracy of multi-step-ahead model predictions compares with trivial predictors and changes with the horizon. |
Nonlinearity¶
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Computes the nonlinearity measure L through nsAMDF (nonlinear average magnitude difference function), developed by Ozkurt et al. [1]. |
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Normalized drop-one-out constant interpolation nonlinear prediction error. |
Reconstructs the time series as a time-delay embedding, and performs Principal Components Analysis on the result. |
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Singular Spectrum Analysis of a time series. |
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Modified 0-1 test for chaos. |
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How densely the delay-embedded trajectory is sampled around each of its points, and how that density changes along the orbit. |
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Correlation dimension and entropy from the TISEAN package's |
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Poincare section analysis of a time series. |
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Optimal delay time using the method of Parlitz and Wichard. |
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How the box-counting (order-2 Renyi) entropy of a delay embedding grows with embedding dimension. |
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How well nearby delay vectors predict their target value, compared with surrogates. |
Box-counting and correlation-sum estimates of the dimension of the delay embedding, and how they change with the embedding dimension. |
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The local dimension and persistence of the reconstructed attractor, from extreme-value statistics of close returns. |
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Whether the time-delay embedding of the series forms separate clusters of points. |
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Kernel PCA of a time-delay embedding of the series, compared with linear PCA. |
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How the fraction of false nearest neighbors falls as the embedding dimension increases. |
The spectrum of generalized (fractal) dimensions of the delay embedding, estimated from nearest-neighbor distances. |
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How the number of close pairs of points in the delay embedding grows with distance (the correlation sum and its scaling). |
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Largest Lyapunov exponent: how nearest-neighbor trajectories diverge, and the scaling of that divergence. |
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The spectrum of Lyapunov exponents of the delay-embedded trajectory. |
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Persistent homology of the delay embedding: the lifetimes of its loops and components. |
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Recurrence quantification analysis (RQA) of the delay-embedded series. |
Recurrence-time statistics from a recurrence plot. |
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Analysis of the histogram of return times. |
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Takens' estimator of the correlation dimension, at the length scale enclosing a fixed fraction of pairs. |
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Information dimension by the fixed-mass method (TISEAN's |
Physics¶
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Simulates a hypothetical walker moving through the time domain. |
Couple a time series to a driven dynamical system. |
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How the series' average drift and noise intensity depend on its current level, from its increments. |
Pre-Process¶
How time-series properties change after a preprocessing step. |
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How time-series properties change as a preprocessing step is applied more and more strongly. |
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How the error of an AR model changes after preprocessing the series. |
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Nonlinear noise reduction, and how it changes the series. |
Scaling¶
Implements fluctuation analysis by a variety of methods. |
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Scale-dependent estimates of multifractal scaling in a time series. |
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Higuchi's fractal dimension of a time series. |
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Multifractal detrended fluctuation analysis (MFDFA): the multifractal spectrum of a time series. |
Spectral¶
Cross-frequency phase-amplitude coupling. |
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Statistics of the power spectrum of a time series. |
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Statistics of the Fourier phase spectrum of a time series. |
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Separates the power spectrum into aperiodic (1/f) and periodic (oscillatory) components. |
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Cepstral statistics: harmonic (comb) structure of the power spectrum. |
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Quadratic phase coupling between frequencies, from the squared bicoherence. |
Statistics of the amplitude envelope of the full series and of its dominant oscillation. |
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Multi-scale fluctuation analysis of the instantaneous phase of the dominant oscillation. |
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Fit sinusoids or a Fourier series to the time series. |
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Time-varying spectral statistics from a spectrogram. |
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Phase-persistence ("rhythmicity") spectrum of a time series. |
Stationarity¶
Compares the distribution in consecutive time-series segments. |
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How stationarity estimates depend on the number of time-series subsegments. |
Correlations between simple statistics in local windows of a time series. |
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Basic statistics about an input time series. |
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How local maximums and minimums vary across the time series. |
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Performs the KPSS (Kwiatkowski-Phillips-Schmidt-Shin) stationarity test. |
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Analyze how the time-series range changes across time. |
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Measures mean drift by analyzing mean and variance in time-series subsegments. |
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Compare local statistics to global statistics of a time series. |
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Goodness of a polynomial fit to a time series |
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Length of an input data vector. |
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Standard deviation of the nth derivative of the time series. |
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Quantifies various measures of trend in a time series. |
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Simple mean-stationarity metric using the StatAv measure. |
Sliding window measures of stationarity. |
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Monotonic trend ('ramping') in windowed statistics. |
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Slow feature analysis of windowed statistics. |
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Phillips-Perron unit-root test statistics and p-values. |
Statistics on the prominences of, and intervals between, the peaks of a time series. |
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Drift in a lag-tau (auto)correlation via a cumulative-sum test. |
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Drift in the mean, via a cumulative-sum (CUSUM) test. |
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How local statistics vary across many overlapping segments of the time series. |
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How the output of |
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Cross-forecast errors of zeroth-order time-series models. |
Surrogates¶
Analyzes test statistics obtained from surrogate time series. |
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Surrogate data test of a nonlinear statistic, tc3 or trev (hctsa's |
Symbolic¶
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Quantifies how surprised you would be of the next data point given recent memory. |
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Compute local motifs in a binary symbolization of the input time series. |
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Motifs in a coarse-graining of a time series to a 3-letter alphabet. |
Homogeneity of the gaps between like symbols in a binarized time series. |
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Compute statistics on a binary symbolisation of the input time series. |
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Transition probabilities between time-series states. |
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How transition probabilities change with alphabet size. |
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Coarse-grains a continuous time series to a discrete alphabet. |
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Binary run-length statistics normalized against an AR(1) null. |
Wavelet¶
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Wavelet decomposition of the time series. |
Detail coefficients of a wavelet decomposition. |
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Continuous wavelet transform of a time series. |
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Discrete wavelet transform coefficients. |
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Frequency components in a periodic time series. |
Estimates of the fractal index (Hurst exponent) of a signal. |
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Multiscale variance decomposition via the maximal overlap DWT. |
Adaptive best-basis wavelet packet decomposition. |