A Comparison on Parameter Estimation in the First-Order Autoregressive Process Having Non-Normal Errors and Additive Outliers

Abstract

Abstract

This paper presents an estimator for an unknown mean AR(1) process having non-normal errors and additive outliers and compares this estimator with other existing estimators. We apply the double recursive median adjustment to the weighted symmetric estimator. Five estimators are considered as follows: the weighted symmetric estimator (_), the Guo’s estimator (_), the recursive mean adjusted weighted symmetric estimator (_), the recursive median adjusted weighted symmetric estimator (_) and the double recursive median adjusted weighted symmetric estimator (_). The mean square error (MSE) of estimators is compared via simulation studies. Simulation results have shown that the proposed estimator, _ , provides a MSE lower than those of the other estimators when _ is in the range of about 0.3 to 0.6, and the errors have the _ , exponential(1)-1 and uniform(-1,1) distribution. For the 0.9N(0,1)+0.1N(0,100) errors, the _ outperforms the others in terms of the MSE when _ is close to one.

Keywords: parameter estimation; autoregressive process; non-normal errors, additive outliers