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

Title & Authors
ON THE COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES GENERATED BY ρ*-MIXING SEQUENCES
Ko, Mi-Hwa; Kim, Tae-Sung; Ryu, Dae-Hee;

Abstract
Let {$\small{Y_{ij}-{\infty}\;}$<$\small{\;i\;}$<$\small{\;{\infty}}$} be a doubly infinite sequence of identically distributed and $\small{{\rho}^*}$-mixing random variables with zero means and finite variances and {$\small{a_{ij}-{\infty}\;}$<$\small{\;i\;}$<$\small{\;{\infty}}$} an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of {$\small{{\sum}^n_{k=1}\;{\sum}^{\infty}_{i=-{\infty}}\;a_{i+k}Y_i/n^{1/p}}$; $\small{n\;{\geq}\;1}$} 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 $\small{{\rho}^*}$-mixing case.
Keywords
moving average process;complete moment convergence;$\small{{\rho}^*}$-mixing;moment inequality;
Language
English
Cited by
1.
Complete moment convergence of widely orthant dependent random variables*, Communications in Statistics - Theory and Methods, 2016, 0
2.
Convergence of Moving Average Processes for Dependent Random Variables, Communications in Statistics - Theory and Methods, 2011, 40, 13, 2366
3.
Complete moment convergence for moving average process generated by ρ − $\rho^{-}$ -mixing random variables, Journal of Inequalities and Applications, 2015, 2015, 1
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