We study the asymptotic behavior of the integrated periodogram for $\alpha$-stable linear processes. For $\alpha \epsilon (1, 2)$ we prove a functional limit theorem for the integrated periodogram. The limit is an $\alpha$-stable analogue to the Brownian bridge. We apply our results to investigate some specific goodness-of-fit tests for heavy-tailed linear processes.
Publié le : 1996-10-14
Classification:
Linear process,
moving average process,
stable process,
frequency domain,
integrated periodogram,
functional limit theorem,
quadratic form,
goodness-of-fit test,
62M15,
62G07,
60F17,
62M10
@article{1069362301,
author = {Kl\"uppelberg, Claudia and Mikosch, Thomas},
title = {The integrated periodogram for stable processes},
journal = {Ann. Statist.},
volume = {24},
number = {6},
year = {1996},
pages = { 1855-1879},
language = {en},
url = {http://dml.mathdoc.fr/item/1069362301}
}
Klüppelberg, Claudia; Mikosch, Thomas. The integrated periodogram for stable processes. Ann. Statist., Tome 24 (1996) no. 6, pp. 1855-1879. http://gdmltest.u-ga.fr/item/1069362301/