ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ*-MIXING SEQUENCES

Abstract

Let {<TEX>$Y_{ij}-{\infty}\;</TEX><TEX><</TEX><TEX>\;i\;</TEX><TEX><</TEX><TEX>\;{\infty}$</TEX>} be a doubly infinite sequence of identically distributed and <TEX>${\rho}^*$</TEX>-mixing random variables with zero means and finite variances and {<TEX>$a_{ij}-{\infty}\;</TEX><TEX><</TEX><TEX>\;i\;</TEX><TEX><</TEX><TEX>\;{\infty}$</TEX>} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {<TEX>${\sum}^n_{k=1}\;{\sum}^{\infty}_{i=-{\infty}}\;a_{i+k}Y_i/n^{1/p}$</TEX>; <TEX>$n\;{\geq}\;1$</TEX>} under some suitable conditions. We extend Theorem 1.1 of Li and Zhang [Y. X. Li and L. X. Zhang, Complete moment convergence of moving average processes under dependence assumptions, Statist. Probab. Lett. 70 (2004), 191.197.] to the <TEX>${\rho}^*$</TEX>-mixing case.