Figure 2.

Illustration of the link between network Granger causality and parameters of SVAR models. (a) Lag matrices $A^1,\dots ,A^d$ and inverse covariance matrix of the innovation, ${\Sigma }^{-1}$, of an SVAR model. Nonzero entries of $A^k$ and ${\Sigma }^{-1}$ are shaded. (b) Expanded graphical model, which replicates variables over time. (c) Compact graphical model combining all interactions from past lags. In both graphs, Granger causal interactions (solid edges) correspond to nonzero entries in $A^k$ and instantaneous causal effects (dashed undirected edges) correspond to nonzero entries in ${\Sigma }^{-1}$. Abbreviation: SVAR, structural vector autoregressive.