pyhctsa.operations.correlation.embed2_dist¶

pyhctsa.operations.correlation.embed2_dist(y, tau=None)¶

Analyzes distances in a 2-dimensional embedding space of a time series.

Returns statistics on the sequence of successive Euclidean distances between points in a two-dimensional time-delay embedding space with a given time-delay, tau.

Outputs include the autocorrelation of distances, the mean distance, the spread of distances, and statistics from an exponential fit to the distribution of distances.

Parameters:¶

y : array-like¶

The z-scored input time series.

tau : int or str, optional¶

The time delay: an integer number of samples, or a rule that sets it from the series: 'tau' (or 'ac'; the first zero crossing of the autocorrelation function), 'ac1e' (the floor of its first 1/e crossing) or 'mi' (the smaller of the first minimum of the Kraskov automutual information and the 'ac1e' delay); see get_tau(). A delay set by a rule is capped at N/10; if it cannot be set the output is NaN. If None, 'tau'. Default is None.

Returns:¶

A dictionary containing various statistics of the embedding including the autocorrelation of distances, the mean distance, the spread of distances, and statistics from an exponential fit to the distribution of distances. d_cv is the mean of the distances divided by their standard deviation (the reciprocal of the coefficient of variation). d_expfit_meandiff is the mean absolute difference between the histogram of distances (equal-width bins, their number the larger of the Sturges and Freedman-Diaconis rules, normalized as a probability density) and the fitted exponential density at the bin centers; NaN if all the distances are equal.

Return type:¶

dict