Applications of the CLT for Positively Associated Random Process in Time Series Analysis

Abstract

This paper explores the implications of the Central Limit Theorem (CLT) within the framework of positively associated stationary random fields, which are pivotal in mathematical statistics, reliability theory, percolation, and statistical physics. It delves into the challenges of extending the CLT's convergence rate to these complex fields, building upon the foundational work by Newman and subsequent contributions. The study presents a novel approach to constructing ARMA models that align with the CLT, offering a robust framework for time series analysis. The paper concludes with the significance of these findings for statistical modeling and forecasting in various disciplines.