Precise asymptotics for the moment convergence of moving-average process under dependence
Bull. Korean Math. Soc. 2010 Vol. 47, No. 3, 585-592
https://doi.org/10.4134/BKMS.2010.47.3.585
Published online May 1, 2010
Qing-Pei Zang and Ke-Ang Fu
Jiangsu University and Zhejiang Gongshang University
Abstract : Let $\{\varepsilon_i: -\infty < i < \infty\}$ be a strictly stationary sequence of linearly positive quadrant dependent random variables and $\sum_{i=-\infty}^{\infty}|a_{i}|<\infty$. In this paper, we prove the precise asymptotics in the law of iterated logarithm for the moment convergence of moving-average process of the form $X_{k}=\sum_{i=-\infty}^{\infty}a_{i+k}\varepsilon_{i}, k \geq 1$.
Keywords : precise asymptotics, moving-average, linear positive quadrant dependence
MSC numbers : 60F99, 60G20
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