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

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.