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In this paper, we perform the first comparison of a large variety of effective connectivity measures in detecting causal effects among observed interacting systems based on their statistical significance. Well-known measures estimating direction and strength of interdependence between time series are compared: information theoretic measures, model-based multivariate measures in the time and frequency domains, and phase-based measures. The performance of measures is tested on simulated data from three systems: three coupled Hénon maps; a multivariate autoregressive (MVAR) model with and without EEG as an exogenous input; and simulated EEG. No measure was consistently superior. Measures that model the data as MVAR perform well when the data are drawn from that model. Frequency domain measures perform well when the data have a clearly defined band of interest. When neither of these is true, information theoretic measures perform well. Overall, the measure with the best performance in a variety of situations and with a low computational cost is conditional Granger causality. Partial Granger causality and multivariate Granger causality are also good measures, but their computational cost rises rapidly with the number of channels. Copula Granger causality can also be used reliably, but its computational cost rises rapidly with the number of data.

Original publication




Journal article


Comput Biol Med

Publication Date





Biomedical signal processing, Connectivity, EEG