Convergence rates for probabilities of moderate deviations for moving average processes

The present paper first shows that, without any dependent structure assumptions for a sequence of random variables, the refined results of the complete convergence for the sequence is equivalent to the corresponding complete moment convergence of the sequence. Then this paper investigates the convergence rates and refined convergence rates (or complete moment convergence) for probabilities of moderate deviations of moving average processes. The results in this paper extend and generalize some well-known results.