Limiting behaviour of moving average processes under \(\varphi \)-mixing assumption. (English) Zbl 1154.60026

Summary: Let \(\{Y_i, - \infty <i<\infty \}\) be a doubly infinite sequence of identically distributed \(\varphi \)-mixing random variables, \(\{a_i, - \infty <i<\infty \}\) be 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 moving average processes \(\{X_n = \sum_{i=-\infty}^\infty a_iY_{i+n}, n \geq 1\}\) based on the sequence \(\{Y_i, - \infty <i<\infty \}\) of \(\varphi \)-mixing random variables, improving the result of [Zhang, L., 1996. Complete convergence of moving average processes under dependence assumptions. Statist. Probab. Lett. 30, No. 2, 165–170 (1996; Zbl 0873.60019)].


60F15 Strong limit theorems


Zbl 0873.60019
Full Text: DOI


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