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

Tailen Hsing

doi:10.1214/aop/1022677460

July 1999 On the Asymptotic Distributions of Partial Sums of Functionals of Infinite-Variance Moving Averages

Tailen Hsing

Ann. Probab. 27(3): 1579-1599 (July 1999). DOI: 10.1214/aop/1022677460

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.

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Tailen Hsing "On the Asymptotic Distributions of Partial Sums of Functionals of Infinite-Variance Moving Averages," The Annals of Probability 27(3), 1579-1599, (July 1999). https://doi.org/10.1214/aop/1022677460

Published: July 1999

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