Open Access
Translator Disclaimer
June 2006 On discriminating between long-range dependence and changes in mean
István Berkes, Lajos Horváth, Piotr Kokoszka, Qi-Man Shao
Ann. Statist. 34(3): 1140-1165 (June 2006). DOI: 10.1214/009053606000000254


We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly dependent with one change in mean at an unknown point, and under the alternative it is long-range dependent. We compute the CUSUM statistic Tn, which allows us to construct an estimator of a change-point. We then compute the statistic Tn,1 based on the observations up to time and the statistic Tn,2 based on the observations after time . The statistic Mn=max [Tn,1,Tn,2] converges to a well-known distribution under the null, but diverges to infinity if the observations exhibit long-range dependence. The theory is illustrated by examples and an application to the returns of the Dow Jones index.


Download Citation

István Berkes. Lajos Horváth. Piotr Kokoszka. Qi-Man Shao. "On discriminating between long-range dependence and changes in mean." Ann. Statist. 34 (3) 1140 - 1165, June 2006.


Published: June 2006
First available in Project Euclid: 10 July 2006

zbMATH: 1112.62085
MathSciNet: MR2278354
Digital Object Identifier: 10.1214/009053606000000254

Primary: 62G10 , 62M10

Keywords: Change-point in mean , CUSUM , long-range dependence , variance of the mean

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 3 • June 2006
Back to Top