Assessing frequency domain causality in cardiovascular time series with instantaneous interactions

The partial directed coherence (PDC) is commonly used to assess in the frequency domain the existence of causal relations between two time series measured in conjunction with a set of other time series. Although the multivariate autoregressive (MVAR) model traditionally used for PDC computation accounts only for lagged effects, instantaneous effects cannot be neglected in the analysis of cardiovascular time series.

We propose the utilization of an extended MVAR model for PDC computation, in order to improve the evaluation of frequency domain causality in the presence of zero-lag correlations among multivariate time series.

A procedure for the identification of a MVAR model combining instantaneous and lagged effects is introduced. The coefficients of the extended model are used to estimate an extended PDC (EPDC). EPDC is compared to the traditional PDC on a simulated MVAR process and on real cardiovascular variability series.

Simulation results evidence that the presence of zero-lag correlations may produce misleading PDC profiles, while the correct causality patterns can be recovered using EPDC. Application on real data leads to spectral causality estimates which are better interpretable in terms of the known cardiovascular physiology using EPDC than PDC.

This study emphasizes the necessity of including instantaneous effects in the MVAR model used for the computation of PDC in the presence of significant zero-lag correlations in multivariate time series.