Granger Causality in High-Dimensional Networks of Time Series

TL;DR

This paper introduces a spectral dynamic PCA-based method to identify directed causal connections in high-dimensional brain networks, effectively isolating specific node interactions by removing confounding influences from other nodes.

Contribution

It presents a novel spectral PCA approach for causality detection in high-dimensional networks, addressing confounding effects and demonstrating applicability to EEG data.

Findings

Effective in simulations for complex time series networks

Successfully applied to multichannel EEG networks

Outperforms existing causality analysis methods

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.