## The Annals of Statistics

### On discriminating between long-range dependence and changes in mean

#### Abstract

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.

#### Article information

Source
Ann. Statist. Volume 34, Number 3 (2006), 1140-1165.

Dates
First available: 10 July 2006

Permanent link to this document
http://projecteuclid.org/euclid.aos/1152540745

Digital Object Identifier
doi:10.1214/009053606000000254

Zentralblatt MATH identifier
1112.62085

Mathematical Reviews number (MathSciNet)
MR2278354

#### Citation

Berkes, István; Horváth, Lajos; Kokoszka, Piotr; Shao, Qi-Man. On discriminating between long-range dependence and changes in mean. The Annals of Statistics 34 (2006), no. 3, 1140--1165. doi:10.1214/009053606000000254. http://projecteuclid.org/euclid.aos/1152540745.

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