Limiting behaviour of moving average processes genenrated by negatively dependent random variables under sub-linear expectations

Abstract

Let $\{Y_i,-\infty <i<\infty \}$ be a doubly infinite sequence of identically distributed, negatively dependent random variables under sub-linear expectations, $\{a_i,-\infty <i<\infty \}$ be an absolutely summable sequence of real numbers. In this article, we study complete convergence and Marcinkiewicz-Zygmund strog law of large numbers for the partial sums of moving average processes $\{X_n={\sum }_{i=-\infty }^{\infty }{a}_i{Y}_{i+n},n\ge 1\}$ based on the sequence $\{Y_i,-\infty <i<\infty \}$ of identically distributed, negatively dependent random variables under sub-linear expectations, complementing the result of [Chen, et al., 2009. Limiting behaviour of moving average processes under $\phi$-mixing assumption. Statist. Probab. Lett. 79, 105-111].

13 pagess, submitted to Statistics and Probability letters