pyhctsa.operations.correlation.embed2_angle_tau

pyhctsa.operations.correlation.embed2_angle_tau(y, max_tau)

Angle autocorrelation in a 2-dimensional delay embedding, over delays.

Investigates how the autocorrelation of the angles between successive points in the two-dimensional delay embedding (y[t], y[t + tau]) changes as tau varies from 1, 2, …, max_tau. For each tau the angle of each step is measured from the horizontal, as in embed2(), and its autocorrelation is taken at lags 1, 2 and 3. A step between two coincident points (a repeated pair of values) has no direction (0/0), so its angle is undefined and is removed from the sequence of angles before the autocorrelations are computed. The outputs summarize the three resulting curves as a function of tau.

Parameters:
y : array-like

The input time series.

max_tau : int

The maximum time delay to consider.

Returns:

  • ac1_thetaac1, ac1_thetaac2, ac1_thetaac3: the lag-1 autocorrelation (across tau) of the lag-1, lag-2 and lag-3 angle autocorrelations

  • mean_thetaac1, mean_thetaac2, mean_thetaac3: their means across tau

  • max_thetaac1, … and min_thetaac1, …: their maxima and minima

  • meanrat_thetaac12: the ratio mean_thetaac1 / mean_thetaac2

  • diff_thetaac12: the sum across tau of the absolute difference between the lag-2 and lag-1 angle autocorrelations

All are NaN if an angle autocorrelation is undefined at any tau (e.g., when no step at that tau has a defined angle, or all of its angles are equal). A scalar NaN is returned if the series is too short to embed.

Return type:

dict