On model fitting and estimation of strictly stationary processes

TL;DR

This paper proposes a novel approach to modeling strictly stationary processes using an AR(1) characterization instead of traditional ARMA models, providing consistent and asymptotically normal estimators.

Contribution

It introduces an AR(1) based modeling framework for stationary processes and derives estimators with proven statistical properties.

Findings

AR(1) characterization effectively models various stationary processes

Derived estimators are consistent and asymptotically normal

Challenges the conventional ARMA modeling approach

Abstract

Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are considered, modeling is traditionally based on fitting an autoregressive moving average (ARMA) process. However, we challenge this conventional approach. Instead of fitting an ARMA model, we apply an AR(1) characterization in modeling any strictly stationary processes. Moreover, we derive consistent and asymptotically normal estimators of the corresponding model parameter.