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

TL;DR

This paper introduces a bootstrap-based test for independence between stationary time series using distance covariance, capable of detecting any dependence within a specified lag, and demonstrates its superior performance through simulations.

Contribution

It develops a novel bootstrap test for time series independence based on distance covariance, extending Wasserstein distance bounds to $\

Findings

The test outperforms existing methods in simulations.

The bootstrap procedure's validity is established under $\

Theoretical bounds for Wasserstein distance are generalized to $\

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 $\alpha$-mixing. Previous results of this kind only existed for i.i.d. processes.