Periodic moving averages of random variables with regularly varying tails

• 成果类型: Article
• 署名作者: Anderson, PL; Meerschaert, MM
• 署名单位: Albion College; Nevada System of Higher Education (NSHE); University of Nevada Reno
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1997
• 页码: 771-785
• 关键词: infinite variance; limit theory; parameter-estimation; time-series; models

摘要

In this paper we establish the basic asymptotic theory for periodic moving averages of i.i.d. random variables with regularly varying tails. The moving average coefficients are allowed to vary according to the season. A simple reformulation yields the corresponding results for moving averages of random vectors. Our main result is that when the underlying random variables have finite variance but infinite fourth moment, the sample autocorrelations are asymptotically stable. It is well known in this case that sample autocorrelations in the classical stationary moving average model are asymptotically normal.