A novel method for estimating the parameter of a Gaussian AR(1) process with additive outliers

A novel estimator for a Gaussian first-order autoregressive [AR(1)] process with additive outliers is presented. A recursive median adjustment based on an alpha-trimmed mean was applied to the weighted symmetric estimator. The following estimators were considered: the weighted symmetric estimator ((rho) over cap (W)), the recursive-mean-adjusted weighted symmetric estimator ((rho) over cap (R-W)), the recursive-median-adjusted weighted symmetric estimator ((rho) over cap (Rmd-W)), and the weighted symmetric estimator using adjusted recursive median based on the alpha-trimmed mean ((rho) over cap (Tm-Rmd-W)). Using Monte Carlo simulations, the mean square errors (MSE) of the estimators were compared. Simulation results showed that the proposed estimator, (rho) over cap (Tm-Rmd-W), provided a smaller MSE than those from (rho) over cap (W), (rho) over cap (R-W) and (rho) over cap (Rmd-W) for almost all situations.