Multivariate out-of-sample tests for Granger causality

A time series is said to Granger cause another series if it has incremental predictive power when forecasting it. While Granger causality tests have been studied extensively in the univariate setting, much less is known for the multivariate case. In this paper we propose multivariate out-of-sample tests for Granger causality. The performance of the out-of-sample tests is measured by a simulation study and graphically represented by Size-Power plots. It emerges that the multivariate regression test is the most powerful among the considered possibilities. As a real data application, we investigate whether the consumer confidence index Granger causes retail sales in Germany, France, the Netherlands and Belgium.