COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES WITH DEPENDENT INNOVATIONS

Title & Authors
COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES WITH DEPENDENT INNOVATIONS
Kim, Tae-Sung; Ko, Mi-Hwa; Choi, Yong-Kab;

Abstract
Let $\small{{Y_i;-\infty}$<$\small{i}$<$\small{\infty}}$ be a doubly infinite sequence of identically distributed and $\small{\phi}$-mixing random variables with zero means and finite variances and $\small{{a_i;-\infty}$<$\small{i}$<$\small{\infty}}$ an absolutely summable sequence of real numbers. In this paper, we prove the complete moment convergence of $\small{{{\sum}_{k=1}^{n}\;{\sum}_{i=-\infty}^{\infty}\;a_{i+k}Y_i/n^{1/p};n\geq1}}$ under some suitable conditions.
Keywords
moving average process;complete moment convergence$\small{\phi}$-mixing;
Language
English
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