Journal of Inequalities and Applications
Volume 2011 (2011), Article ID 320932, 17 pages
doi:10.1155/2011/320932
Research Article

Precise Asymptotics in the Law of Iterated Logarithm for Moving Average Process under Dependence

Jie Li1,2

1Wang Yanan Institute for Studies in Economics, Xiamen University, Xiamen 361005, China
2School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, China

Received 10 November 2010; Revised 2 February 2011; Accepted 3 March 2011

Academic Editor: Ulrich Abel

Copyright © 2011 Jie Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let { 𝜉 𝑖 , − ∞ < 𝑖 < ∞ } be a doubly infinite sequence of identically distributed and 𝜙 -mixing random variables, and let { 𝑎 𝑖 , − ∞ < 𝑖 < ∞ } 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 = ∑ + ∞ 𝑖 = − ∞ 𝑎 𝑖 + 𝑘 𝜉 𝑖 , 𝑘 ≥ 1 } , which extend Liu and Lin's (2006) result to moving average process under dependence assumption.