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Measures of linear dependence (coherence) and nonlinear dependence (phasesynchronization) between any number of multivariate time series are defined.The measures are expressed as the sum of lagged dependence and instantaneousdependence. The measures are non-negative, and take the value zero only whenthere is independence of the pertinent type. These measures are defined in thefrequency domain and are applicable to stationary and non-stationary timeseries. These new results extend and refine significantly those presented in aprevious technical report (Pascual-Marqui 2007, arXiv:0706.1776 [stat.ME],http://arxiv.org/abs/0706.1776), and have been largely motivated by the seminalpaper on linear feedback by Geweke (1982 JASA 77:304-313). One important fieldof application is neurophysiology, where the time series consist of electricneuronal activity at several brain locations. Coherence and phasesynchronization are interpreted as "connectivity" between locations. However,any measure of dependence is highly contaminated with an instantaneous,non-physiological contribution due to volume conduction and low spatialresolution. The new techniques remove this confounding factor considerably.Moreover, the measures of dependence can be applied to any number of brainareas jointly, i.e. distributed cortical networks, whose activity can beestimated with eLORETA (Pascual-Marqui 2007, arXiv:0710.3341 [math-ph]).

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