Power of change-point tests for long-range dependent data
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We investigate the power of the CUSUM test and the Wilcoxon change-point
tests for a shift in the mean of a process with long-range dependent noise. We derive analytic
formulas for the power of these tests under local alternatives. These results enable us to
calculate the asymptotic relative efficiency (ARE) of the CUSUM test and the Wilcoxon
change point test. We obtain the surprising result that for Gaussian data, the ARE of these
two tests equals 1, in contrast to the case of i.i.d. noise when the ARE is known to be 3/Pi.
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asymptotic relative efficiency of tests, change-point problems, functional limit theorem, local alternatives, long memory, long-range dependent data, nonparametric change-point tests, power of test, Wilcoxon two-sample rank test