Assessing directional interactions among multiple physiological time series: The role of instantaneous causality

This paper deals with the assessment of frequency domain causality in multivariate (MV) time series with significant instantaneous interactions. After providing different causality definitions, we introduce an extended MV autoregressive modeling approach whereby each definition is described in the time domain in terms of the model coefficients, and is quantified in the frequency domain by means of novel measures of directional connectivity. These measures are illustrated in a theoretical example showing how they reduce to known indexes when instantaneous causality is trivial, while they describe peculiar aspects of directional interaction in the presence of instantaneous causality. The application on real MV cardiovascular and EEG time series is then reported to investigate the role played by instantaneous causality in the practical evaluation of frequency domain connectivity.