Robust discrimination between long-range dependence and a change in mean
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Date
2018
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Abstract
In this paper we introduce a robust to outliers Wilcoxon change-point testing procedure,
for distinguishing between short-range dependent time series with a change in mean at unknown
time and stationary long-range dependent time series. We establish the asymptotic
distribution of the test statistic under the null hypothesis for L1 near epoch dependent
processes and show its consistency under the alternative. The Wilcoxon-type testing procedure
similarly as the CUSUM-type testing procedure of Berkes, Horvath, Kokoszka and
Shao (2006), requires estimation of the location of a possible change-point, and then using
pre- and post-break subsamples to discriminate between short and long-range dependence.
A simulation study examines the empirical size and power of the Wilcoxon-type testing
procedure in standard cases and with disturbances by outliers. It shows that in standard
cases the Wilcoxon-type testing procedure behaves equally well as the CUSUM-type testing
procedure but outperforms it in presence of outliers.
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Keywords
Wilcoxon change-point test statistic, long-range dependence, near epoch dependence, change-point