Geodesic
Complete $q$-order moment convergence of moving average processes under $\varphi $-mixing assumptions
Applications of Mathematics, Tome 59 (2014) no. 1, pp. 69-83.

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Let $\{Y_i, -\infty $ be a doubly infinite sequence of identically distributed $\varphi $-mixing random variables, and $\{a_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 $ of $\varphi $-mixing random variables under some suitable conditions. These results generalize and complement earlier results.
DOI : 10.1007/s10492-014-0042-x
Classification : 60F15, 60G50
Keywords: moving average; $\varphi $-mixing; complete convergence; $q$-order moment; maximum of partial sums 
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Zhou, Xing-Cai; Lin, Jin-Guan. Complete $q$-order moment convergence of moving average processes under $\varphi $-mixing assumptions. Applications of Mathematics, Tome 59 (2014) no. 1, pp. 69-83. doi : 10.1007/s10492-014-0042-x. http://geodesic.mathdoc.fr/articles/10.1007/s10492-014-0042-x/

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