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We propose a testing procedure based on the Wilcoxon two-sample teststatistic in order to test for change-points in the mean of long-rangedependent data. We show that the corresponding self-normalized test statisticconverges in distribution to a non-degenerate limit under the hypothesis thatno change occurred and that it diverges to infinity under the alternative of achange-point with constant height. Furthermore, we derive the asymptoticdistribution of the self-normalized Wilcoxon test statistic under localalternatives, that is under the assumption that the height of the level shiftdecreases as the sample size increases. Regarding the finite sampleperformance, simulation results confirm that the self-normalized Wilcoxon testyields a consistent discrimination between hypothesis and alternative and thatits empirical size is already close to the significance level for moderatesample sizes.

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