An identifiable model to assess frequency-domain granger causality in the presence of significant instantaneous interactions.

We present a new approach for the investigation of Granger causality in the frequency domain by means of the partial directed coherence (PDC). The approach is based on the utilization of an extended multivariate autoregressive (MVAR) model, including instantaneous effects in addition to the lagged effects traditionally studied, to fit the observed multiple time series prior to PDC computation. Model identification is performed combining standard MVAR coefficient estimation with a recent technique for instantaneous causal modeling based on independent component analysis. The approach is first validated on simulated MVAR processes showing that, in the presence of instantaneous effects, only the extended model is able to interpret the imposed Granger causality patterns, while the traditional MVAR approach may yield strongly biased PDC estimates. The subsequent application to multichannel EEG time series confirms the potentiality of the approach in real data applications, as the importance of instantaneous effects led to significant differences in the PDC estimated after traditional and extended MVAR identification.