Journal of the
Korean Mathematical Society JKMS

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 $\{\sum_{k=1}^n \sum_{i=-\infty}^\infty a_{i+k} Y_i/n^{1/p} ; n \geq 1\}$ under some suitable conditions.

Keywords: moving average process, complete moment convergence, $\phi$-mixing

MSC numbers: 60G50, 60F15