Persistence-robust Granger causality testing

The observed persistence common in economic time series may arise from a variety of models that are not always distinguished with confidence in practice, yet play an important role in model specification and second stage inference procedures. Previous literature has introduced causality tests with conventional limiting distributions in I(0)/I(1)VAR models with unknown integration orders, based on an additional surplus lag in the specification of the estimated equation, which is not included in the tests. Building on this approach, but using an infinite order VARX framework, we provide a highly persistence-robust Granger causality test that accommodates i.a. stationary, nonstationary, local-to-unity, long-memory, and certain (unmodelled) structural break processes in the forcing variables within the context of a single Chi-Squared null limiting distribution. No first stage testing or estimation is required and known lag orders are not assumed.