Testing independence for multivariate time series via auto multivariate distance covariance

We propose the auto multivariate distance covariance for time series, which extends the concept of joint high distance covariance. Furthermore, we develop two new procedures for testing mutual independence in multivariate time series that combine the auto multivariate distance covariance with either the Box and Pierce (1970) or the Li and McLeod (1981) tests. Simulation results suggest that the proposed method is highly effective. We also apply our methods to analyze the relationships between the real gross domestic products of the United Kingdom, Canada, and the United States.