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

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 Zhang , P. , Shaman , P. ( 1995 ). Assessing prediction error in autoregressive models . Trans. Amer. Mathemat. Soc. 347 : 627 – 637 .Crossref], Web of Science ®] , Google Scholar]) and Kabaila and He (1999 Kabaila , P. , He , Z. ( 1999 ). On assessing prediction error in autoregressive models . J. Time Ser. Anal. 20 : 663 – 670 .Crossref] , Google Scholar]) 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.