A Central Limit Theorem for Randomly Indexed $m$-Dependent Random Variables

Yilun Shang

We prove a central limit theorem for the sum of a random number $N_n$ of $m$-dependent random variables. The sequence $N_n$ and the terms in the sum are not assumed to be independent. Moreover, the conditions of the theorem are not stringent in the sense that a simple moving average sequence serves as an example.