pyhctsa.operations.correlation.crinkle_statistic¶

pyhctsa.operations.correlation.crinkle_statistic(y)¶

Crinkle statistic: normalized fourth moment of the second difference.

With \(\tilde{x} = x - \bar{x}\),

\[C = \frac{\langle (\tilde{x}_{t-1} - 2\tilde{x}_t + \tilde{x}_{t+1})^4 \rangle} {\langle \tilde{x}_t^2 \rangle^{2}},\]

where the numerator averages over the \(N - 2\) interior points and the denominator over all \(N\) samples. Statistic as used in D. Kaplan’s code (hctsa DK_crinkle), where it is credited to J. Theiler.

Parameters:¶

y : array-like¶

The input time series.

Returns:¶

The crinkle statistic (NaN if the series is constant or has fewer than three samples, where it is undefined).

Return type:¶

float