  Granger causality is a commonly used method for uncovering information flow
and dependencies in a time series. Here we introduce JGC (Jacobian Granger
Causality), a neural network-based approach to Granger causality using the
Jacobian as a measure of variable importance, and propose a thresholding
procedure for inferring Granger causal variables using this measure. The
resulting approach performs consistently well compared to other approaches in
identifying Granger causal variables, the associated time lags, as well as
interaction signs. Lastly, through the inclusion of a time variable, we show
that this approach is able to learn the temporal dependencies for nonstationary
systems whose Granger causal structures change in time.
