• change-point problem;
  • functional limit theorem;
  • long memory;
  • long-range dependent data;
  • non-parametric test;
  • Wilcoxon two-sample rank test

Abstract.  We propose a non-parametric change-point test for long-range dependent data, which is based on the Wilcoxon two-sample test. We derive the asymptotic distribution of the test statistic under the null hypothesis that no change occurred. In a simulation study, we compare the power of our test with the power of a test which is based on differences of means. The results of the simulation study show that in the case of Gaussian data, our test has only slightly smaller power minus.3pt than the ‘difference-of-means’ test. For heavy-tailed data, our test outperforms the ‘difference-of-means’ test.