Gaussian limit fields for the integrated periodogram
Authors:
- Claudia KlöppelbergCKClaudia Klöppelberg
- Thomas MikoschTMThomas Mikosch
Open Access
- 1 August 1996
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 6 (3) , 969-991
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.Keywords
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