Moment inequality and complete convergence of moving average processes under asymptotically linear negative quadrant dependence assumptions

Abstract

Let {Y, Y _i , −∞ < i < ∞} be a doubly infinite sequence of identically distributed and asymptotically linear negative quadrant dependence random variables, {a _i , −∞ < i < ∞} an absolutely summable sequence of real numbers. We are inspired by Wang et al. (Econometric Theory 18:119–139, 2002) and Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003). And Salvadori (Stoch Environ Res Risk Assess 17:116–140, 2003) have obtained Linear combinations of order statistics to estimate the quantiles of generalized pareto and extreme values distributions. In this paper, we prove the complete convergence of \({\left\{ {{\sum\nolimits_{k = 1}^n {{\sum\nolimits_{i = - \infty }^\infty {a_{{i + k}} Y_{i} /n^{{1/t}} } }} },n \geq 1} \right\}}\) under some suitable conditions. The results obtained improve and generalize the results of Li et al. (1992) and Zhang (1996). The results obtained extend those for negative associated sequences and ρ^*-mixing sequences.