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 SN = ∑ N n=1 [K(Xn) - EK(Xn)], as N→ ∞, where [Xn] is a moving average stable process and K is a bounded and measurable function. The results show that SN follows a central or non-central limit theorem depending on the rate at which the moving average coefficients tend to 0.