Testing for independence: Permutation based tests vs. BDS test

The aim of this paper is bringing a bit of light on the problem of testing independence for time series. We make a comparative study of the well-known BDS test versus the new tests based on permutations that have been recently developed by several authors. Our study shows that even for purely deterministic time series the tests systematically fails and therefore the assertion "test A is better than test B" cannot be done and the use of several tests may help to avoid the fact of making wrong conclusions.