pyhctsa.operations.nonlinearity.nsamdf¶

pyhctsa.operations.nonlinearity.nsamdf(x, tau_mult=2, win_len_rel=10, shift_len_rel=0.5, degree=7)¶

Computes the nonlinearity measure L through nsAMDF (nonlinear average magnitude difference function), developed by Ozkurt et al. [1].

The lag range and window of the nsAMDF are set from the time series’ own correlation time: with tau the first zero-crossing of the autocorrelation function, the maximum lag is ceil(tau_mult*tau) and the window length win_len_rel times that. The normalized curves of the nsAMDF for p = 2 and p = degree are compared by their root-mean-square difference.

This function was authored by Tolga Esat Ozkurt, 2020. (tolgaozkurt@gmail.com). Edits by Ben Fulcher for incorporating into hctsa and Joshua Moore for incorporating into pyhctsa.

References

Parameters:¶

x : array-like¶

Input time series.

tau_mult : float or int¶

The maximum lag, as a multiple of the first zero-crossing of the autocorrelation function. Default is 2.

win_len_rel : float or int¶

The window length, as a multiple of the maximum lag (a long enough segment is important to estimate the nonlinearity). Default is 10.

shift_len_rel : float or int¶

The shift between successive windows, as a proportion of the window length (window length minus overlap). Default is 0.5.

degree : int¶

The chosen degree p should ideally be large enough to capture the highest order of nonlinearity within the data. Default is 7.

Returns:¶

L, the nsAMDF nonlinearity measure: the root-mean-square difference between the nsAMDF curves for p = 2 and p = degree, each normalized by its maximum (so it is invariant to the scale of the series). Returns NaN if the autocorrelation function has no zero-crossing, or the window is longer than the time series.

Return type:¶

dict