Robust Discrimination between Long-Range Dependence and a Change in Mean

TL;DR

This paper presents a robust Wilcoxon change-point test to distinguish between short-range dependent series with mean shifts and stationary long-range dependence, outperforming traditional methods in outlier scenarios.

Contribution

It introduces a robust Wilcoxon-based change-point detection method with proven asymptotic properties for differentiating dependence types in time series.

Findings

The Wilcoxon test performs comparably to CUSUM in standard cases.

It outperforms CUSUM in the presence of outliers.

Application to hydrologic data demonstrates practical utility.

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, Horv\'ath, 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.