On a functional central limit theorem for stationary linear processes generated by associated processes

Abstract

A functional central limit theorem is obtained for a stationary linear process of the form $X_t = \sum_{j=0}^\infty a_j \epsilon_{t-j}$, where $\{\epsilon_t \}$ is a strictly stationary associated sequence of random variables with $E \epsilon_t =0,~E (\epsilon_t^2 )< \infty$ and $\{a_j \}$ is a sequence of real numbers with $\sum_{j=0}^\infty |a_j |<\infty.$ A central limit theorem for a stationary linear process generated by stationary associated processes is also discussed.