Abstract
In this thesis, we first review some previous results about complete convergence and complete moment convergence of moving average processes under dependence ($\varphi-mixing$ or negatively associated) and independence assumption. And then we show that the complete moment convergence of the maximal partial sums of moving average processes $\{\sum_{i=-\infty}^{\infty}a_iY_{i+n},n\geq 1\}$ under the assumption that $\{Y_{i},-\infty<i<\infty\}$ is a sequence of identically distributed $\varphi-mixing$ random variables.