Further research on complete moment convergence for moving average process of a class of random variables

In this article, the complete moment convergence for the partial sum of moving average processes {Xn=∑i=−∞∞aiYi+n,n≥1}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{X_{n}=\sum_{i=-\infty}^{\infty}a_{i}Y_{i+n},n\geq 1\}$\end{document} is established under some mild conditions, where {Yi,−∞<i<∞}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{Y_{i},-\infty < i<\infty\}$\end{document} is a doubly infinite sequence of random variables satisfying the Rosenthal type maximal inequality and {ai,−∞<i<∞}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\{a_{i},-\infty< i<\infty\}$\end{document} is an absolutely summable sequence of real numbers. These conclusions promote and improve the corresponding results given by Ko (J. Inequal. Appl. 2015:225, 2015).