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We investigate the power of the CUSUM test and the Wilcoxon change-point testfor a shift in the mean of a process with long-range dependent noise. We deriveanalytiv formulas for the power of these tests under local alternatives. Theseresults enable us to calculate the asymptotic relative efficiency (ARE) of theCUSUM test and the Wilcoxon change point test. We obtain the surprising resultthat for Gaussian data, the ARE of these two tests equals 1, in contrast to thecase of i.i.d. noise when the ARE is known to be $3/\pi$.

Power of Change-Point Tests for Long-Range Dependent Data