Directed wavelet covariance

A causal wavelet decomposition of the covariance structure for bivariate locally stationary processes, named directed wavelet covariance, is introduced and discussed. Theoretically, when compared to Fourier-based quantities, wavelet-based estimators are more appropriate to non-stationary processes and processes with local patterns, outliers and rapid regime changes. Results of directed coherence (DC), wavelet coherence (WTC) and directed wavelet covariance (DWC) with simulated data are also presented. All three quantities could identify the simulated covariances structures. Finally, an illustration of the proposed directed wavelet covariance in a task-based EEG experiment is given.