Connectivity Inference between Neural Structures via Partial Directed Coherence

This paper describes the rigorous asymptotic distributions of the recently introduced partial directed coherence (PDC) – a frequency domain description of Granger causality between multivariate time series represented by vector autoregressive models. We show that, when not zero, PDC is asymptotically normally distributed and therefore provides means of comparing different strengths of connection between observed time series. Zero PDC indicates an absence of a direct connection between time series, and its otherwise asymptotically normal behavior degenerates into that of a mixture of variables allowing the computation of rigorous thresholds for connectivity tests using either numerical integration or approximate numerical methods. A Monte Carlo study illustrates the power of the test under PDC nullity. An analysis of electroencephalographic data, before and during an epileptic seizure episode, is used to portray the usefulness of the test in a real application.