A distance-based test of independence between two multivariate time series

Abstract

We contribute to recent research on distance correlation by extending its capability to test for independence between two time series. The proposed test is a Portmanteau-type test based on double-centered distance cross-covariances. We show that the test statistic constructed in this way is asymptotically normal and pivotal under the null hypothesis of independence, and it is consistent under fixed alternative hypotheses of dependence. We also propose a fast wild bootstrap procedure that can significantly improve the performance of the asymptotic test in finite samples. An extensive Monte Carlo simulation study designed to compare the proposed test with other existing procedures shows that both the proposed test and its bootstrap version can achieve a good size and power performance for several data generating processes (DGPs), and they can significantly outperform other tests under model misspecification. An empirical application to illustrate the applicability of the proposed method is also given.