pyhctsa.operations.nonlinearity.tisean_d2¶

pyhctsa.operations.nonlinearity.tisean_d2(y, tau=1, maxm=10, theiler_win=0.01)¶

Correlation dimension and entropy from the TISEAN package’s d2 routine.

Estimates the correlation sum, the correlation dimension and the correlation entropy of the time series [1], then summarises the results.

Takens’ estimator [2] is computed for the correlation dimension, along with related statistics: other dimension estimates obtained by finding suitable scaling ranges, and a search for a flat region in the output of TISEAN’s h2 algorithm, which indicates determinism/deterministic chaos [3].

To find a suitable scaling range, a penalized regression procedure is used to determine an optimal scaling range that simultaneously spans the greatest range of scales and shows the best fit to the data, and return the range, a goodness of fit statistic, and a dimension estimate.

Unlike hctsa, which shells out to installed TISEAN binaries, this runs the vendored TISEAN sources in-process (see pyhctsa.toolboxes.Tisean_3_0_1.tisean).

References

Parameters:¶

y : array-like¶

Input time series.

tau : int or str, optional¶

The time-delay. Can be an integer, or 'ac' for the first zero-crossing of the autocorrelation function, or 'mi' for the first minimum of the automutual information. Default is 1.

maxm : int, optional¶

The maximum embedding dimension. Default is 10.

theiler_win : int or float, optional¶

The Theiler window. A value in (0, 1) is taken as a proportion of the time-series length. Default is 0.01, i.e. 1% of the data length.

Returns:¶

Statistics summarising Takens’ estimator, the local slopes of the correlation sum (raw and Gaussian-kernel smoothed), and the correlation entropy. Returns NaN if the time series is too short.

Return type:¶

dict or float