Testing for the mean shifts for long memory time series in presence of breaks in variance

Abstract

This paper considers the detection problem of mean shifts in presence of variance changes for long memory time series. In performing the test, we employ the Ratio test introduced by Horváth L. et al. (2008). Given for the case of breaks in variance, the asymptotic properties of the tests are established. It is shown that the test statistics are not robust due to neglected of variance changes. And the numerical simulation results are consistent with our theoretical analysis.