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. We show that the corresponding self-normalized test statistic
converges in distribution to a non-degenerate limit under the hypothesis that
no change occurred and that it diverges to infinity under the alternative of a
change-point with constant height. Furthermore, we derive the asymptotic
distribution of the self-normalized Wilcoxon test statistic under local
alternatives, that is under the assumption that the height of the level shift
decreases as the sample size increases. Regarding the finite sample
performance, simulation results confirm that the self-normalized Wilcoxon test
yields a consistent discrimination between hypothesis and alternative and that
its empirical size is already close to the significance level for moderate
sample sizes
