Equivalent Conditions of Complete Moment Convergence of Weighted Sums for ϕ-Mixing Sequence of Random Variables

Abstract

In this article, the complete moment convergence of weighted sums for ϕ-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete moment convergence of weighted sums for ϕ-mixing sequence of random variables are established. These results promote and improve the corresponding results obtained by Li et al. (1995) and Gut (1993) from i.i.d. to ϕ-mixing setting. Moreover, we obtain the complete moment convergence of moving average processes based on ϕ-mixing random variables, which extends the result of Kim et al. (2008) in the sense that it does not require a specific mixing rate.