pyhctsa.operations.stationarity.monotonic_trend¶

pyhctsa.operations.stationarity.monotonic_trend(y, max_points=2000)¶

Monotonic trend of a time series against time: the Mann-Kendall test and the Theil-Sen slope.

Kendall’s tau between the series and the sample index measures how consistently the series rises (tau near 1) or falls (tau near -1) over the record, whatever the shape of the rise (no p-value is reported: under the serial correlation of a typical time series the independent-samples p-value of tau is not a test, only a transform of tau and the length); the Theil-Sen slope, the median of the slopes between all pairs of samples, is a robust counterpart of the least-squares gradient (trend()), insensitive to outliers and to a few extreme samples at either end of the record.

Parameters:¶

y : array-like¶

The input time series.

max_points : int, optional¶

The Theil-Sen slope uses every pair of samples when the series has at most this many samples; a longer series is subsampled to max_points evenly spaced samples first (the median of about two million pairwise slopes), using the samples’ true time differences. Kendall’s tau always uses the whole series. Default is 2000.

Returns:¶

Dictionary containing:

• ’tau’: Kendall’s tau-b between the series and time (the Mann-Kendall statistic, normalised to [-1, 1]).

• ’sen_slope’: The Theil-Sen slope, in units of the series per sample.

All NaN for a constant series or one with fewer than 3 samples.

Return type:¶

dict

Notes

Mann (1945), Econometrica 13, 245; Kendall (1970), Rank Correlation Methods, 4th ed.; Theil (1950), Proc. KNAW 53, 386; Sen (1968), J. Am. Stat. Assoc. 63, 1379. pyhctsa-only: hctsa has no monotonic-trend statistic at the sample level (ramping_windows() applies Kendall’s tau to windowed statistics across ten segments).