Improvement in Parameter Estimation for a Gaussian AR(1) Process with an Unknown Drift and Additive Outliers: A Simulation Study

Abstract

This paper presents a new parameter estimation for a Gaussian first-order autoregressive (AR(1)) process with an unknown drift and additive outliers. Recursive median adjustment was applied based on an α-winsorized mean to the weighted symmetric estimator. The following estimators were considered: the weighted symmetric estimator (ρˆW), the recursive mean adjusted weighted symmetric estimator (ρˆ_R–W), the recursive median adjusted weighted symmetric estimator (ρ_ˆRmd–W), and the weighted symmetric estimator using the adjusted recursive median, based on the α-winsorized mean (ρˆ_W–Rmd–W). Using Monte Carlo simulations, the mean square error (MSE) of estimators were compared. Simulation results
showed that the proposed estimator, ρˆ_W–Rmd–W, provided an MSE lower than those of ρˆ_W–Rmd–W, and ρˆ_W–Rmd–W for almost all situations.