Granger causality is an established measure of the “causal influence” that one statistical process has on another. It has been used extensively in neuroscience to infer statistical causal influences. Recently, however, many works in the neuroscience literature have begun to compare Granger causal influences along forward and reverse links of a feedback network in order to determine the direction of information flow in this network.
We asked whether comparing Granger causal influences correctly captures the direction of information flow in a simple feedback network. We discovered, using simple theoretical experiments, that comparison of Granger causal influences can, in fact, yield an answer that is opposite to the true direction of information flow.