Abstract
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.
Citation
Claudia Klöppelberg. Thomas Mikosch. "Gaussian limit fields for the integrated periodogram." Ann. Appl. Probab. 6 (3) 969 - 991, August 1996. https://doi.org/10.1214/aoap/1034968236
Information