# COMPLETE MOMENT CONVERGENCE OF MOVING AVERAGE PROCESSES WITH DEPENDENT INNOVATIONS

• Kim, Tae-Sung ;
• Ko, Mi-Hwa ;
• Choi, Yong-Kab
• Published : 2008.03.31
• 67 11

#### Abstract

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

#### Keywords

moving average process;complete moment convergence$\phi$-mixing

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