The sample autocorrelations of heavy-tailed processes with applications to arch

• 成果类型: Article
• 署名作者: Davis, RA; Mikosch, T
• 署名单位: Colorado State University System; Colorado State University Fort Collins; University of Groningen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 2049-2080
• 关键词: moving averages; limit theory; CONVERGENCE; BEHAVIOR

摘要

We study the sample ACVF and ACF of a general stationary sequence under a weak mixing condition and in the case that the marginal distributions are regularly varying. This includes linear and bilinear processes with regularly varying noise and ARCH processes, their squares and absolute values. We show that the distributional limits of the sample ACF can be random, provided that the Variance of the marginal distribution is infinite and the process is nonlinear. This is in contrast to infinite variance linear processes. If the process has a finite second but infinite fourth moment, then the sample ACP is consistent with scaling rates that grow at a slower rate than the standard root n. Consequently, asymptotic confidence bands are wider than those constructed in the classical theory. We demonstrate the theory in full detail far an ARCH(1) process.