ASYMPTOTICS FOR LINEAR-PROCESSES

• 成果类型: Article
• 署名作者: PHILLIPS, PCB; SOLO, V
• 署名单位: Macquarie University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348666
• 发表日期: 1992
• 页码: 971-1001
• 关键词: central limit theorems; Moving averages; time-series; invariance principles; random-variables

摘要

A method of deriving asymptotics for linear processes is introduced which uses an explicit algebraic decomposition of the linear filter. The technique is closely related to Gordin's method but has some advantages over it, especially in terms of its range of application. The method offers a simple unified approach to strong laws, central limit theory and invariance principles for linear processes. Sample means and sample covariances are covered. The results accommodate both homogeneous and heterogeneous innovations as well as innovations with undefined means and variances.