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.

翻译：我们提出了一种基于距离协方差的自助法程序来检验两个严格平稳时间序列的独立性。该检验能在任意最大滞后阶数$L$内检测两个时间序列之间的任意依赖性。模拟研究表明，我们的检验优于其他替代检验方法。在证明所用自助法程序的有效性时，我们推广了在$\alpha$-混合假设下经验测度与其边际分布之间的Wasserstein距离的界。此前此类结论仅适用于独立同分布过程。