Asymptotics for moving average processes with dependent innovations

Let X-t be a moving average process defined by X-t = Sigma (infinity)(k=0) psik epsilon (t-k), t = 1,2,..., where the innovation {epsilon (k)} is a centered sequence of random variables and {psi (k)} is a sequence of real numbers. Under conditions on {psi (k)} which entail that {X-t} is either a long memory process or a linear process, we study asymptotics of the partial sum process Sigma X-[ns](t=0)t For a long memory process with innovations forming a martingale difference sequence, the functional limit theorems of Sigma X-[ns](t=0)t (properly normalized) are derived. For a linear process, we give sufficient conditions so that normalized) converges weakly to a standard Brownian motion if the corresponding Sigma ([ns])(k=1) is true. The applications to fractional processes and other mixing innovations are also discussed. (C) 2001 Elsevier Science BY. All rights reserved.