The integrated periodogram for stable processes

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.