Asymptotic normality for random sums of linear processes

Abstract

Let X j = Σ ∞ j=0 b j ε i− j , for i= 1,2,3,…, be the consecutive obeservations of stationary linear processes, with Eε i =0, Eε 2 i = σ 2 and E| ε i | 3 < ∞, and let {N n,n∈ N} be a sequence of integer-valued random variables defined on the same probability space as {ε j, i∈ Z} . Under mild conditions on the process, asymptotic normality is established for the random sum, S N n= Σ N n i= 1X i , of linear processes. Statistical applications of the result are also discussed.