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.
Publié le : 1996-08-14
Classification:
Moving average process,
spectral distribution,
integrated periodogram,
functional central limit theorem,
Gaussian field,
Kiefer process,
empirical process,
sample autocovariance,
changepoint,
60F17,
60G60,
60G10,
62M15
@article{1034968236,
author = {Kl\"oppelberg, Claudia and Mikosch, Thomas},
title = {Gaussian limit fields for the integrated periodogram},
journal = {Ann. Appl. Probab.},
volume = {6},
number = {1},
year = {1996},
pages = { 969-991},
language = {en},
url = {http://dml.mathdoc.fr/item/1034968236}
}
Klöppelberg, Claudia; Mikosch, Thomas. Gaussian limit fields for the integrated periodogram. Ann. Appl. Probab., Tome 6 (1996) no. 1, pp. 969-991. http://gdmltest.u-ga.fr/item/1034968236/