  This manuscript presents a novel method for discovering effective
connectivity between specified pairs of nodes in a high-dimensional network of
time series. To accurately perform Granger causality analysis from the first
node to the second node, it is essential to eliminate the influence of all
other nodes within the network. The approach proposed is to create a
low-dimensional representation of all other nodes in the network using
frequency-domain-based dynamic principal component analysis (spectral DPCA).
The resulting scores are subsequently removed from the first and second nodes
of interest, thus eliminating the confounding effect of other nodes within the
high-dimensional network. To conduct hypothesis testing on Granger causality,
we propose a permutation-based causality test. This test enhances the accuracy
of our findings when the error structures are non-Gaussian. The approach has
been validated in extensive simulation studies, which demonstrate the efficacy
of the methodology as a tool for causality analysis in complex time series
networks. The proposed methodology has also been demonstrated to be both
expedient and viable on real datasets, with particular success observed on
multichannel EEG networks.
