Limit theorems for quadratic forms with applications to Whittle's estimate

• 成果类型: Article
• 署名作者: Horváth, L; Shao, QM
• 署名单位: Utah System of Higher Education; University of Utah; University of Oregon
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 1999
• 页码: 146-187
• 关键词: long-range dependence; linear variables; time-series

摘要

We establish strong and weak approximations for quadratic forms of weakly and strongly dependent random variables and obtain necessary and sufficient conditions for the weak convergence of weighted functions of quadratic forms. The results are applied to get the asymptotic distributions of some tests which can be used to detect possible changes in the long-memory parameter.