Cross-scale / cross-frequency causality

First, the multiscale time series are decomposed using
complex continuous wavelet transform.
We use the algorithm of Torrence and Compo, codes available at github.
Then, phases and amplitudes of selected scales/periods/frequencies
are obtained from wavelet coefficients as described, e.g., in
Palus, M.: Cross-Scale Interactions and Information Transfer
Entropy 16(10), 5263-5289, 2014. -- doi:10.3390/e16105263

The instantaneous phases can be used for the inference of phase-phase causality
using the equiquantal binning estimator for the conditional mutual information:
FORTRAN code .

For the phase-amplitude causality we recommend the estimator for the conditional
mutual information with 3-dimensional condition: FORTRAN code .

Note that this is a Gaussian estimator and uses soubroutines svdcmp and pythag
from Numerical Recipes which I cannot distribute.

© Milan Palus 2023