Central limit theorem for linear processes

Abstract

In this paper we study the CLT for partial sums of a generalized linear process Xn = ∑ni=1 ani ξi, where sup n ∑ni=1 a2ni < ∞, max1 ≤ i ≤ n|ani| → 0 as n → ∞ and ξi's are in turn, pairwise mixing martingale differences, mixing sequences or associated sequences. The results are important in analyzing the asymptotical properties of some estimators as well as of linear processes.