Granger causality and contiguity between stochastic processes

Although according to many econometricians the definition of causality proposed by Granger differs from other definitions of causation in the philosophy of science, in this Letter we argue that it is not completely lacking in philosophical legitimacy. We attempt to shed new light on the nexus between Granger causality and the concept of contiguity. In particular, we prove that the existence of a Granger causal link between two stochastic processes requires that these be “contiguous” or that there exist a chain of processes, one contiguous to the next, which link the two processes.