GAUSSIAN LIMIT FIELDS FOR THE INTEGRATED PERIODOGRAM
成果类型：
Article
署名作者：
Kluppelberg, Claudia; Mikosch, Thomas
署名单位：
Johannes Gutenberg University of Mainz; University of Groningen
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
969-991
关键词：
摘要：
Functionals of a two-parameter integrated periodogram have been used for detecting a change in the spectral distribution of a stationary sequence. The bases for these results are functional central limit theorems for the integrated periodogram with a Gaussian limit field. We prove functional central limit theorems for a general linear sequence having a finite fourth moment which is shown to be the optimal moment condition. Our approach is via an approximation of the integrated periodogram by a finite linear combination of sample autocovariances. This gives special insight into the structure of the Gaussian limit field.