A novel method for estimating the parameter of a Gaussian AR(1) process with additive outliers
2011 Issue 01
A novel estimator for a Gaussian first-order autoregressive [AR(1)] process with additive outliers is presented. A recursive median adjustment based on an -trimmed mean was applied to the weighted symmetric estimator. The following estimators were considered: the weighted symmetric estimator (ˆ W ), the recursive-mean-adjusted weighted symmetric estimator (ˆ R W ), the recursive-median-adjusted weighted symmetric estimator (ˆ Rmd W ), and the weighted symmetric estimator using adjusted recursive median based on the -trimmed mean (ˆ Tm Rmd W ). Using Monte Carlo simulations, the mean square errors (MSE) of the estimators were compared. Simulation results showed that the proposed estimator, ˆ Tm Rmd W , provided a smaller MSE than those fromˆWfromˆfromˆW , ˆ R W andˆRmdandˆandˆRmd W for almost all situations.
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