A CENTRAL LIMIT THEOREM FOR LINEAR PROCESSES UNDER LINEAR NEGATIVELY QUADRANT DEPENDENCE

Abstract. In this paper we establish a central limit theorem for weighted sums of Yn = ∑n i=1 an,iXi, where {an,i, n ∈ N, 1 ≤ i ≤ n} is an array of nonnegative numbers such that supn≥1 ∑n i=1 a 2 n,i < ∞, max1≤i≤n an,i → 0 and {Xi, i ∈ N} is a sequence of linear negatively quadrant dependent random variables with EXi = 0 and EX2i < ∞. Using this result we will obtain a central limit theorem for partial sums of linear processes. 1