Instantaneous and lagged measurements of linear and nonlinear dependence between groups of multivariate time series: frequency decomposition

Understand

Measures of linear dependence (coherence) and nonlinear dependence (phase synchronization) between any number of multivariate time series are defined.

• The measures are expressed as the sum of lagged dependence and instantaneous dependence.
• The measures are non-negative, and take the value zero only when there is independence of the pertinent type.
• These measures are defined in the frequency domain and are applicable to stationary and non-stationary time series.