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 variable selection procedure for inferring Granger causal variables with this measure, using criteria of significance and consistency. The resulting approach performs consistently well compared to other approaches in identifying Granger causal variables, the associated time lags, as well as interaction signs. In addition, we also discuss the need for contemporaneous variables in Granger causal modeling as well as how these neural network-based approaches reduce the impact of nonseparability in dynamical systems, a problem where predictive information on a target variable is not unique to its causes, but also contained in the history of the target variable itself.

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