pyhctsa.operations.correlation.trev

pyhctsa.operations.correlation.trev(y, tau='ac')

Normalized nonlinear autocorrelation (trev) function of a time series.

Calculates the trev function, a normalized nonlinear autocorrelation, as described in the TSTOOL nonlinear time-series analysis package. This quantity is often used as a nonlinearity statistic in surrogate data analysis, see [1].

Method as implemented in the TSTOOL package for nonlinear time-series analysis (C. Merkwirth, U. Parlitz, I. Wedekind, D. Engster and W. Lauterborn; GNU GPL), here re-implemented through hctsa’s CO_trev.

References

Parameters:
y : array-like

Input time series.

tau : int or str, optional

Time lag. Can be:

  • int: Use the specified lag.

  • ’ac’: Use the first zero-crossing of the autocorrelation function.

  • ’ac1e’: Use the floor of the first 1/e crossing of the autocorrelation function.

  • ’mi’: Use the smaller of the first minimum of the (Kraskov) automutual information and the ‘ac1e’ delay (see get_tau()).

Default is 'ac'. If the delay cannot be set from the series the output is NaN.

Returns:

Dictionary containing:

  • ’raw’: The raw trev expression.

  • ’abs’: The magnitude of the raw expression.

  • ’num’: The numerator.

  • ’absnum’: The magnitude of the numerator.

  • ’denom’: The denominator.

Return type:

dict