The Annals of Probability

On the Asymptotic Distributions of Partial Sums of Functionals of Infinite-Variance Moving Averages

Tailen Hsing

Abstract

This paper investigates the asymptotic distribution of the partial sum, $S_N=\sum_{n=1}^N [K(X_n)-EK(X_n)]$, as $N \to \infty$, where ${X_n}$ is a moving average stable process and $K$ is a bounded and measurable function. The results show that $S_N$ follows a central or non-central limit theorem depending on the rate at which the moving average coefficients tend to 0.

Article information

Source
Ann. Probab., Volume 27, Number 3 (1999), 1579-1599.

Dates
First available in Project Euclid: 29 May 2002

https://projecteuclid.org/euclid.aop/1022677460

Digital Object Identifier
doi:10.1214/aop/1022677460

Mathematical Reviews number (MathSciNet)
MR1733161

Zentralblatt MATH identifier
0961.60038

Subjects
Primary: 60F05.

Citation

Hsing, Tailen. On the Asymptotic Distributions of Partial Sums of Functionals of Infinite-Variance Moving Averages. Ann. Probab. 27 (1999), no. 3, 1579--1599. doi:10.1214/aop/1022677460. https://projecteuclid.org/euclid.aop/1022677460

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