Limiting behaviour of moving average processes genenrated by negatively dependent random variables under sub-linear expectations (2207.11884v1)

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 $\varphi$-mixing assumption. Statist. Probab. Lett. 79, 105-111].