A robust test for mean change in dependent observations

Ruibing Qin,Weiqi Liu

doi:10.1186/s13660-015-0569-8

Abstract

A robust test based on the indicators of the data minus the sample median is proposed to detect the change in the mean of α-mixing stochastic sequences. The asymptotic distribution of the test is established under the null hypothesis that the mean μ remains as a constant. The consistency of the proposed test is also obtained under the alternative hypothesis that μ changes at some unknown time. Simulations demonstrate that the test behaves well for heavy-tailed sequences.

Highlights

The problem of a mean change at an unknown location in a sequence of observations has received considerable attention in the literature
Most of the existing results in the statistic and econometric literature have concentrated on the case that the innovations are Gaussian
Many economic and financial time series can be very heavy-tailed with infinite variances; see e.g. Mittnik and Rachev [ ]

Summary

Introduction

The problem of a mean change at an unknown location in a sequence of observations has received considerable attention in the literature. De Jong et al [ ] proposed a robust KPSS test based on the ‘sign’ of the data minus the sample median, which behaves rather well for heavy-tailed series. We detect change in the mean of a sequence, so Assumption holds under the null hypothesis and the alternative one.

Results

Conclusion