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We present a test for independence of two strictly stationary time seriesbased on a bootstrap procedure for the distance covariance. Our test detectsany kind of dependence between the two time series within an arbitrary maximumlag $L$. In simulation studies, our test outperforms alternative testingprocedures. In proving the validity of the underlying bootstrap procedure, wegeneralise bounds for the Wasserstein distance between an empirical measure andits marginal distribution under the assumption of $\alpha$-mixing. Previousresults of this kind only existed for i.i.d. processes.

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