Kernel Methods for Nonlinear Connectivity Detection

In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model adequacy. As a consequence, the canonical methodology for model construction, diagnostics, and Granger connectivity inference applies with no change other than computation using kernels in lieu of second-order moments.Comment: 14 pages, 14 figures, preliminary version being prepared for submission to a refereed journa

Frequency Domain Repercussions of Instantaneous Granger Causality

Using directed transfer function (DTF) and partial directed coherence (PDC) in the information version, this paper extends the theoretical framework to incorporate the instantaneous Granger causality (iGC) frequency domain description into a single unified perspective. We show that standard vector autoregressive models allow portraying iGC’s repercussions associated with Granger connectivity, where interactions mediated without delay between time series can be easily detected