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 (), the recursive mean adjusted weighted symmetric estimator () proposed by Niwitpong [5], the recursive median adjusted weighted symmetric estimator () proposed by Panichkitkosolkul [6], and the weighted symmetric estimator using adjusted recursive median based on EWMA (). Using Monte Carlo simulations, we compare the mean square error (MSE) of estimators. Simulation results have shown that the proposed estimator, , provides a MSE lower than those of , and  for almost all situations.


Parameter estimation, autoregressive model, recursive median, exponentially weighted moving average, additive outliers

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Last updated: 17 May 2019