Exploring Effective Connectivity by a Granger Causality Approach with Embedded Dimension Reduction.

We propose applying the linear Granger Causality concept to very high-dimensional time series. The approach is based on integrating dimensionality reduction into a multivariate time series model. If residuals of dimensionality reduced models can be transformed back into the original space, prediction errors in the high–dimensional space may be computed, and a Granger Causality Index (GCI) is properly defined. We provide a proof–of–principle, and compare the results with the classical GCI.