Assessing One-Step-Ahead Prediction Error Based on the Median for First-Order Autoregressive Models in the Presence Of Outliers

Abstract

The prediction of the one-step-ahead observation of the first-order autoregressive process in the presence of outliers is considered. The mean square of the prediction error is obtained based on the median estimator of the model parameter for a stationary process. Monte Carlo simulation methods are employed to investigate the performance of the proposed estimator as well as the conventional ordinary least squares estimators proposed by Zhang and Shaman (1995) and Kabaila and He (1999) for a process without outliers. The results show that the proposed method outperforms the conventional method. These conclusions are substantiated with results from actual datasets.

Keywords:

• Conditional prediction error
• Mean square error
• Monte Carlo simulation

2000 Mathematics Subject Classification:

• 62G99
• 62M10

Acknowledgment

This research was supported by NSC-89-2118-M-013-002, Taiwan, R.O.C. (first author) and partially supported by the National Science Foundation (second author). We would like to thank the referees and the Editor for their helpful comments.