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

This chapter develops a predictive approach to Granger causality (GC) testing that utilizes <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="si16.gif"> <mml:mi>k</mml:mi> </mml:math>-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.