Granger Causality in High-Dimensional Networks of Time Series

Abstract: A novel approach is developed for discovering directed connectivity between specified pairs of nodes in a high-dimensional network (HDN) of brain signals. To accurately identify causal connectivity for such specified objectives, it is necessary to properly address the influence of all other nodes within the network. The proposed procedure herein starts with the estimation of a low-dimensional representation of the other nodes in the network utilizing (frequency-domain-based) spectral dynamic principal component analysis (sDPCA). The resulting scores can then be removed from the nodes of interest, thus eliminating the confounding effect of other nodes within the HDN. Accordingly, causal interactions can be dissected between nodes that are isolated from the effects of the network. Extensive simulations have demonstrated the effectiveness of this approach as a tool for causality analysis in complex time series networks. The proposed methodology has also been shown to be applicable to multichannel EEG networks.