title: A framework for assessing frequency domain causality in physiological time series with instantaneous effects.
abstract: We present an approach for the quantification of directional relations in multiple time series exhibiting significant zero-lag interactions. To overcome the limitations of the traditional multivariate autoregressive (MVAR) modelling of multiple series, we introduce an extended MVAR (eMVAR) framework allowing either exclusive consideration of time-lagged effects according to the classic notion of Granger causality, or consideration of combined instantaneous and lagged effects according to an extended causality definition. The spectral representation of the eMVAR model is exploited to derive novel frequency domain causality measures that generalize to the case of instantaneous effects the known directed coherence (DC) and partial DC measures. The new measures are illustrated in theoretical examples showing that they reduce to the known measures in the absence of instantaneous causality, and describe peculiar aspects of directional interaction among multiple series when instantaneous causality is non-negligible. Then, the issue of estimating eMVAR models from time-series data is faced, proposing two approaches for model identification and discussing problems related to the underlying model assumptions. Finally, applications of the framework on cardiovascular variability series and multichannel EEG recordings are presented, showing how it allows one to highlight patterns of frequency domain causality consistent with well-interpretable physiological interaction mechanisms.
authors.affiliation: Department of Physics and BIOtech, University of Trento, 38060 Mattarello, Trento, Italy. luca.faes@unitn.it
authors.forename: Luca
authors.initials: L
authors.lastname: Faes
authors.forename: Silvia
authors.initials: S
authors.lastname: Erla
authors.forename: Alberto
authors.initials: A
authors.lastname: Porta
authors.forename: Giandomenico
authors.initials: G
authors.lastname: Nollo
mesh_terms: D000465:Algorithms; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical
keywords: Granger causality; directed coherence; multivariate autoregressive models; partial directed coherence