RESIDUAL EMPIRICAL PROCESSES FOR LONG AND SHORT MEMORY TIME SERIES

• 成果类型: Article
• 署名作者: Chan, Ngai Hang; Ling, Shiqing
• 署名单位: Chinese University of Hong Kong; Hong Kong University of Science & Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/07-AOS543
• 发表日期: 2008
• 页码: 2453-2470
• 关键词: WEAK-CONVERGENCE; range dependence; limiting distributions; ASYMPTOTIC-EXPANSION; Moving averages; models; estimators; regression; functionals; SEQUENCES

摘要

This paper studies the residual empirical process of long- and short-memory time series regression models and establishes its uniform expansion under a general framework. The results are applied to the stochastic regression models and unstable autoregressive models. For the long-memory noise, it is shown that the limit distribution of the Kolmogorov-Smimov test statistic studied in Ho and Hsing [Ann. Statist. 24 (1996) 992-1024] does not hold when the stochastic regression model includes an unknown intercept or when the characteristic polynomial of the unstable autoregressive model has a unit root. To this end, two new statistics are proposed to test for the distribution of the long-memory noises of stochastic regression models and unstable autoregressive models.