Testing for change-points in long-range dependent time series by means of a self-normalized Wilcoxon test

We propose a testing procedure based on the Wilcoxon two-sample test statistic in order to test for change-points in the mean of long-range dependent data. Under the hypothesis that no change occured, the corresponding self-normalized test statistic converges in distribution to a non-degenerate limit. Under local alternatives, that is under the assumption that a given time series has a change-point in the mean of height $h_n$, the asymptotic distribution of the self-normalized Wilcoxon test statistic can be derived as well. Regarding the finite sample performance of the self-normalized Wilcoxon test, simulation results confirm that empirical size and significance level are already close for moderate sample sizes.