Robust Discrimination between Long-Range Dependence and a Change in Mean
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 $L_1$ 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, Horváth, 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. We also apply both testing procedure to hydrologic data.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.01268
- arXiv:
- arXiv:1804.01268
- Bibcode:
- 2018arXiv180401268G
- Keywords:
-
- Statistics - Methodology;
- 62M10;
- 62F03;
- 62F05;
- 62G35
- E-Print:
- 34 pages, 5 figure, 5 tables