The Annals of Statistics

The integrated periodogram for stable processes

Claudia Klüppelberg and Thomas Mikosch

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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.

Article information

Source
Ann. Statist., Volume 24, Number 5 (1996), 1855-1879.

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362301

Digital Object Identifier
doi:10.1214/aos/1069362301

Mathematical Reviews number (MathSciNet)
MR1421152

Zentralblatt MATH identifier
0898.62116

Subjects
Primary: 62M15: Spectral analysis 62G07: Density estimation
Secondary: 60F17: Functional limit theorems; invariance principles 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

Keywords
Linear process moving average process stable process frequency domain integrated periodogram functional limit theorem quadratic form goodness-of-fit test

Citation

Klüppelberg, Claudia; Mikosch, Thomas. The integrated periodogram for stable processes. Ann. Statist. 24 (1996), no. 5, 1855--1879. doi:10.1214/aos/1069362301. https://projecteuclid.org/euclid.aos/1069362301


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