A Modified Weighted Symmetric Estimator for a Gaussian First-Order Autoregressive Model with Additive Outliers

Guttman and Tiao [1], and Chang [2] showed that the effect of outliers may cause serious bias in estimating autocorrelations, partial correlations, and autoregressive moving average parameters (cited in Chang et al. [3]). This paper presents a modified weighted symmetric estimator for a Gaussian first-order autoregressive AR(1) model with additive outliers. We apply the recursive median adjustment based on an exponentially weighted moving average (EWMA) to the weighted symmetric estimator of Park and Fuller [4]. We consider the following estimators: the weighted symmetric estimator ( ρ̂W ), the recursive mean adjusted weighted symmetric estimator ( ρ̂RW ) proposed by Niwitpong [5], the recursive median adjusted weighted symmetric estimator ( ρ̂RDW ) proposed by Panichkitkosolkul [6], and the weighted symmetric estimator using adjusted recursive median based on EWMA ( ρ̂ − RD EWMA ). Using Monte Carlo simulations, we compare the mean square error (MSE) of estimators. Simulation results have shown that the proposed estimator, ρ̂ − RD EWMA , provides a MSE lower than those of ρ̂W , ρ̂RW and ρ̂RDW for almost all situations.