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

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

Let {$Y_{ij}-{\infty}\;<\;i\;<\;{\infty}$} be a doubly infinite sequence of identically distributed and ${\rho}^*$-mixing random variables with zero means and finite variances and {$a_{ij}-{\infty}\;<\;i\;<\;{\infty}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {${\sum}^n_{k=1}\;{\sum}^{\infty}_{i=-{\infty}}\;a_{i+k}Y_i/n^{1/p}$; $n\;{\geq}\;1$} 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 ${\rho}^*$-mixing case.