pyhctsa.operations.correlation.embed2_basic¶

pyhctsa.operations.correlation.embed2_basic(y, tau=1)¶

Point-density statistics in a two-dimensional delay embedding.

Computes a set of point-density statistics in the embedding space formed by \((y_i, y_{i+\tau})\), with \(y_i\) on the horizontal axis and \(y_{i+\tau}\) on the vertical axis. The method quantifies how points cluster around specific geometric structures in this plane, including diagonals, parabolas, rings, and circles.

The embedding corresponds to a standard two-dimensional delay reconstruction with lag \(\tau\).

Parameters:¶

y : array-like¶

Input time series.

tau : int or str, optional¶

Time delay used to construct the embedding \((y_i, y_{i+\tau})\): an integer number of samples, or a rule that sets it from the series: 'tau' (or 'ac'; the first zero crossing of the autocorrelation function), 'ac1e' (the floor of its first 1/e crossing) or 'mi' (the smaller of the first minimum of the Kraskov automutual information and the 'ac1e' delay); see get_tau(). A delay set by a rule is capped at N/10; if it cannot be set the output is NaN. Default is 1.

Returns:¶

Dictionary of point-density statistics associated with different geometric regions in the embedding space.

Return type:¶

dict