Permutation test of independence in tails for dependent processes

In this article, we propose a permutation test for independence in the tails of two strongly mixing and strictly stationary sequences. We establish the asymptotic validity of the test by demonstrating that both the test statistic and its permutation distribution are asymptotically normal. These results build upon and generalize findings from Basrak and Brborović [1]. Additionally, we conduct a simulation study to evaluate the size and power properties of the proposed test.