Predictive Testing for Granger Causality via Posterior Simulation and Cross-validation

This chapter develops a predictive approach to Granger causality (GC) testing that utilizes $k$-fold cross-validation and posterior simulation to perform out-of-sample testing. A Monte Carlo study indicates that the cross-validation predictive procedure has improved power in comparison to previously available out-of-sample testing procedures, matching the performance of the in-sample F-test while retaining the credibility of post- sample inference. An empirical application to the Phillips curve is provided evaluating the evidence on GC between inflation and unemployment rates.