Limiting behaviour of moving average processes under $\rho$-mixing assumption

Abstract

Let $\{Y_i, -\infty<i<\infty\}$ be a doubly infinite sequence of identically distributed $\rho$-mixing random variables, $\{a_i,-\infty<i< \infty\}$ an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of the moving average processes $\{\sum\limits^\infty_{i=-\infty}a_i Y_{i+n},n\geq1\}$.