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Convergence of moving average processes for dependent random variables. (English) Zbl 1219.60034
Summary: Let \(\{Y _{ i }, - \infty <i < \infty \}\) be a doubly infinite sequence of identically distributed random variables with \(E|Y _{1}| < \infty \), and \(\{a _{ i }, - \infty <i < \infty \}\) be an absolutely summable sequence of real numbers. Under dependence conditions on \(\{Y _{i}\}\), complete convergence and complete moment convergence of moving average process of the form \(X_k = \Sigma^\infty_{i=-\infty} a_{i+k} Y_i\) have been established by many authors. In this article, we give a general method for obtaining the complete moment convergence of the moving average process. Our result extends previous many results from dependent random variables to random variables satisfying some suitable conditions.

MSC:
60F15 Strong limit theorems
62G05 Nonparametric estimation
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