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

摘要

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.