On discriminating between long-range dependence and changes in mean

• 成果类型: Article
• 署名作者: Berkes, Istvan; Horvath, Lajos; Kokoszka, Piotr; Shao, Qi-Man
• 署名单位: Graz University of Technology; Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Utah System of Higher Education; Utah State University; Utah System of Higher Education; University of Utah; University of Oregon; Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000254
• 发表日期: 2006
• 页码: 1140-1165
• 关键词: memory; heteroskedasticity

摘要

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 T-n, which allows us to construct an estimator (k) over cap of a change-point. We then compute the statistic T-n,T-1 based on the observations up to time (k) over cap and the statistic T,2 based on the observations after time (k) over cap. The statistic M-n = max[T-n,T-1, T-n,T-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.