Persistence-robust surplus-lag Granger causality testing

Previous literature has introduced causality tests with conventional limiting distributions in I(0)/I(1) vector autoregressive (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. By extending this surplus lag approach to an infinite order VARX framework,weshow that it can 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 χ2 null limiting distribution.