The Central Limit Theorem for Weakly Dependent Random Variables by the Moment Method

2022/02/09 by Michael Fleermann, Werner Kirsch, Fleermann, Michael +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2202.04717

openalex publication_date 2022/02/09 · openalex created_date 2022/02/13 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study depends solely on the separability of mixed moments. Our investigation yields a new proof for the CLT for α-mixing random variables, but also non-α-mixing random variables fit within our framework, such as MA(∞) processes. In particular, our results can be applied to ARMA(p,q) process with independent white noise.

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