Testing independence for multivariate time series via auto multivariate distance covariance

Abstract.

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.

Keywords:

• auto joint high distance covariance
• multivariate time series
• mutual independence

MSC 2010 subject classifications::

• Primary 62G10
• secondary 62H20

Acknowledgments

The authors thank the editor, associate editor, and two referees for their careful reviews and constructive comments that substantially improve this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Ma’s research was supported by the National Natural Science Foundation of China (Grant No. 12101439).