A Bootstrap Test for Independence of Time Series Based on the Distance Covariance

2021/12/28 by Annika Betken, Betken, Annika, Herold Dehling +3
Economics, Econometrics and Finance · #60F25 #62F40 #Complex Systems and Time Series Analysis #FOS: Mathematics #Primary: 62G10 #Secondary: 62H20 #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2112.14091

openalex publication_date 2021/12/28 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We present a test for independence of two strictly stationary time series based on a bootstrap procedure for the distance covariance. Our test detects any kind of dependence between the two time series within an arbitrary maximum lag L. In simulation studies, our test outperforms alternative testing procedures. In proving the validity of the underlying bootstrap procedure, we generalise bounds for the Wasserstein distance between an empirical measure and its marginal distribution under the assumption of α-mixing. Previous results of this kind only existed for i.i.d. processes.

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