Central limit theorems for moving average processes*

Let $ {{left( {{xi_n}} right)}_{{nin mathbb{Z}}}} $ be a stationary sequence of real random variables with E ξ ₀ = 0 and infinite variance. Furthermore, assume that $ {{left( {{c_n}} right)}_{{nin mathbb{Z}}}} $ is a sequence of real numbers and $ {X_n}=sum {_{{jin mathbb{Z}}}{c_j}{xi_{n-j }}} $ is a moving average processes driven by $ {{left( {{xi_n}} right)}_{{nin mathbb{Z}}}} $ . By using a decomposition of the moving average processes, a central limit theorem for the partial sums $ sumnolimits_{k=1}^n {{X_k}} $ is established. As applications, we obtain some central limit theorems for stationary dependent sequences $ {{left( {{xi_n}} right)}_{{nin mathbb{Z}}}} $ , such as associated sequence, martingale difference, and so on.