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August 1996 Gaussian limit fields for the integrated periodogram
Claudia Klöppelberg, Thomas Mikosch
Ann. Appl. Probab. 6(3): 969-991 (August 1996). DOI: 10.1214/aoap/1034968236


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.


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Claudia Klöppelberg. Thomas Mikosch. "Gaussian limit fields for the integrated periodogram." Ann. Appl. Probab. 6 (3) 969 - 991, August 1996.


Published: August 1996
First available in Project Euclid: 18 October 2002

zbMATH: 0866.60030
MathSciNet: MR1410124
Digital Object Identifier: 10.1214/aoap/1034968236

Primary: 60F17 , 60G60
Secondary: 60G10 , 62M15

Keywords: changepoint , empirical process , functional central limit theorem , Gaussian field , integrated periodogram , Kiefer process , Moving average process , sample autocovariance , Spectral distribution

Rights: Copyright © 1996 Institute of Mathematical Statistics


Vol.6 • No. 3 • August 1996
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