Power of Change-Point Tests for Long-Range Dependent Data
Herold Dehling, Aeneas Rooch, Murad S. Taqqu
TL;DR
This paper analyzes the effectiveness of CUSUM and Wilcoxon change-point tests for detecting mean shifts in long-range dependent data, deriving formulas for their power and efficiency.
Contribution
It provides analytical formulas for the power and asymptotic relative efficiency of these tests under long-range dependence, revealing surprising results for Gaussian data.
Findings
ARE of CUSUM and Wilcoxon tests equals 1 for Gaussian data
Derived formulas for test power under local alternatives
Contrasts long-range dependence with i.i.d. noise case
Abstract
We investigate the power of the CUSUM test and the Wilcoxon change-point test for a shift in the mean of a process with long-range dependent noise. We derive analytiv 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 .
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