Testing for change-points in long-range dependent time series by means of a selfnormalized Wilcoxon test
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Date
2014-09-05
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Abstract
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.
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Keywords
change-point problem, non- parametric test, Wilcoxon test, long-range dependence, self-normalization