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We propose a new measure to estimate the direction of information flux inmultivariate time series from complex systems. This measure, based on the slopeof the phase spectrum (Phase Slope Index) has invariance properties that areimportant for applications in real physical or biological systems: (a) it isstrictly insensitive to mixtures of arbitrary independent sources, (b) it givesmeaningful results even if the phase spectrum is not linear, and (c) itproperly weights contributions from different frequencies. Simulations of aclass of coupled multivariate random data show that for truly unidirectionalinformation flow without additional noise contamination our measure detects thecorrect direction as good as the standard Granger causality. For randommixtures of independent sources Granger Causality erroneously yields highlysignificant results whereas our measure correctly becomes non-significant. Anapplication of our novel method to EEG data (88 subjects in eyes-closedcondition) reveals a strikingly clear front-to-back information flow in thevast majority of subjects and thus contributes to a better understanding ofinformation processing in the brain.

Robustly estimating the flow direction of information in complex physical systems