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Precise asymptotics in the law of iterated logarithm for moving average process under dependence. (English) Zbl 1215.60021

Summary: Let \(\{\xi_i,-\infty<i < \infty\}\) be a doubly infinite sequence of identically distributed and \(\varphi\)-mixing random variables, and let \(\{a_i,-\infty<i<\infty\}\) be an absolutely summable sequence of real numbers. In this paper, we get precise asymptotics in the law of the logarithm for linear process \(\{X_k=\sum^{+\infty}_{i=-\infty} a_{i+k}\xi_i\), \(k \geq 1\}\), which extend W. Liu and Z. Lin’s [Stat. Probab. Lett. 76, No. 16, 1787–1799 (2006; Zbl 1104.60045)] result to moving average process under dependence assumption.

MSC:

60F15 Strong limit theorems

Citations:

Zbl 1104.60045
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References:

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