A central limit theorem for the stationary multivariate linear process generated by associated random vectors

Abstract

A central limit theorem is obtained for a stationary multivariate linearprocess of the form mathbb{X}_{t} = sum_{u=0}^infty A_u mathbb{Z}_{t-u},where {mathbb{Z}_t } is a sequence of strictly stationary m-dimensionalassociated random vectors with {E mathbb{Z}_t = mathbb{O}} and E|mathbb{Z}_t |^2 < inftyand {A_u } is a sequence of coefficient matrices with sum_{u=0}^infty |A_u | < inftyand sum_{u=0}^infty A_u not= O_{m times m}.