Convergence of Moving Average Processes for Dependent Random Variables

Let {Y-i, -infinity < i < infinity} be a doubly infinite sequence of identically distributed random variables with E vertical bar Y-1 vertical bar < infinity, and {a(i), -infinity < i < infinity} be an absolutely summable sequence of real numbers. Under dependence conditions on {Y-i} complete convergence and complete moment convergence of moving average process of the form X-k = Sigma(infinity)(i=-infinity) a(i+k)Y(i) have been established by many authors. In this article, we give a general method for obtaining the complete moment convergence of the moving average process. Our result extends previous many results from dependent random variables to random variables satisfying some suitable conditions.