Summary
Background: 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.
Objectives: 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.
Methods: 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.
Results: 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.
Conclusions: 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.
Keywords
Cardiovascular interactions - Granger causality - partial directed coherence
