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


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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