2.2.2. Auto-correlation for time delay (tau)

This function implements Auto-Correlation (AC) for the selection of the delay tau for permutation entropy. Additionally, it only requires a single time series and has a fast computation time. However, this method is only designed for linear system.

teaspoon.parameter_selection.autocorrelation.autoCorrelation_tau(ts, cutoff=0.36788, AC_method='spearman', plotting=False)[source]

This function takes a time series and uses AC to find the optimum delay based on the correlation being less than a specified cutoff (default is 1/e, which is approximately 0.36788).

Parameters:

  • ts (array) – Time series (1d).

  • cutoff (float) – value for which correlation is considered insignificant (default is 1/e).

  • method (string) – either ‘spearman’ or ‘pearson’. default is ‘spearman’.

Kwargs:

plotting (bool): Plotting for user interpretation. defaut is False.

Returns:

tau, The embedding delay for permutation formation.

Return type:

(int)

The following is an example implementing autocorrelation for selecting tau:

from teaspoon.parameter_selection.autocorrelation import autoCorrelation_tau
import numpy as np

fs = 10
t = np.linspace(0, 100, fs*100)
ts = np.sin(t) + np.sin((1/np.pi)*t)

tau = autoCorrelation_tau(ts, cutoff = 1/np.exp(1), AC_method = 'pearson', plotting = False)
print('Delay from AC: ', tau)

Where the output for this example is:

Delay from AC:   13
../../_images/AC_example.png