Asymptotics for moving average processes with dependent innovations

Let Xt be a moving average process defined by Xt=[summation operator]k=0[infinity][psi]k[var epsilon]t-k, t=1,2,... , where the innovation {[var 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 {Xt} is either a long memory process or a linear process, we study asymptotics of the partial sum process [summation operator]t=0[ns]Xt. For a long memory process with innovations forming a martingale difference sequence, the functional limit theorems of [summation operator]t=0[ns]Xt (properly normalized) are derived. For a linear process, we give sufficient conditions so that [summation operator]t=1[ns]Xt (properly normalized) converges weakly to a standard Brownian motion if the corresponding [summation operator]k=1[ns][var epsilon]k is true. The applications to fractional processes and other mixing innovations are also discussed.