The integrated periodogram for stable processes
Claudia Klüppelberg, Thomas Mikosch
The Annals of Statistics · 1996 · Volume 24 · Issue 5
Abstract
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.
Keywords
60F17, 62G07, 62M10, 62M15, Frequency domain, Functional limit theorem, Goodness-of-fit test, integrated periodogram, linear process, Moving average process, quadratic form, Stable process
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