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Keywords:
moving average; $\varphi $-mixing; complete convergence; $q$-order moment; maximum of partial sums
moving average; $\varphi $-mixing; complete convergence; $q$-order moment; maximum of partial sums
Summary:
Let $\{Y_i, -\infty <i<\infty \}$ be a doubly infinite sequence of identically distributed $\varphi $-mixing random variables, and $\{a_i, -\infty <i<\infty \}$ an absolutely summable sequence of real numbers. We prove the complete $q$-order moment convergence for the partial sums of moving average processes $\Big \{X_n=\sum _{i=-\infty }^\infty a_i Y_{i+n},n\geq 1\Big \}$ based on the sequence $\{Y_i, -\infty <i<\infty \}$ of $\varphi $-mixing random variables under some suitable conditions. These results generalize and complement earlier results.
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