Change-In-Mean Problem for Long Memory Time Series Model

Abstract

In this paper, we propose the ratio test to detect the mean change point in the long-range memory. We proved that the limit distribution of the cumulative sum (CUSUM) statistic under the null hypothesis is a functional of fractional Brownian motion. At the same time, the consistency under the alternative hypothesis is also obtained. Simulations demonstrate that our asymptotic results provide good size and power.