Limiting behaviour of moving average processes under        -mixing assumption

doi:10.1285/i15900932v30n1p17

Limiting behaviour of moving average processes under $\rho$ -mixing assumption

Rita Giuliano Antonini, Tien-Chung Hu, Andrei Volodin

Abstract

Let $\{Y_i, -\infty<i<\infty\}$ be a doubly infinite sequence of identically distributed $\rho$ -mixing random variables, $\{a_i,-\infty<i< \infty\}$ an absolutely summable sequence of real numbers. In this paper, we prove the complete convergence and Marcinkiewicz-Zygmund strong law of large numbers for the partial sums of the moving average processes $\{\sum\limits^\infty_{i=-\infty}a_i Y_{i+n},n\geq1\}$ .

DOI Code: 10.1285/i15900932v30n1p17

Keywords:
moving average; �?-mixing; complete convergence; Marcinkiewicz-Zygmund strong laws of large numbers

Classification: 60F15

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This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.

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Note di Matematica

Limiting behaviour of moving average processes under -mixing assumption

Abstract

Limiting behaviour of moving average processes under $\rho$ -mixing assumption