On Multistep-Ahead Prediction Intervals Following Unit Root Tests for a Gaussian AR(1) Process with Additive Outliers

Recently, Diebold and Kilian [Unit root tests are useful for selecting forecasting models, Journal of Business and Economic Statistics 18, 265-273, 2007] and Niwitpong [Effect of Preliminary unit roots on predictors for an unknown mean AR(1) process, Thailand Statistician 7, 71-79, 2009] indicated that the preciseness of a predictor for an AR(1) process can be increased by using the preliminary unit root tests. This paper extends these mentioned concepts to the multistep-ahead prediction intervals of a Gaussian AR(1) process with additive outliers. The analytic expressions of the coverage probability of prediction intervals are derived and we have proved that the structure of the coverage probability is independent from the mean of the process and the parameter of a random error, but it is a function of an autoregressive parameter and the constant. Additionally, the coverage probabilities and the lengths of the standard prediction interval, the prediction interval following the Dickey-Fuller unit root test and the prediction interval following the Shin et al. unit root test are also compared via simulation studies. Simulation results have shown that the unit root test can improve the accuracy of the multistep-ahead prediction intervals for a near non-stationary AR(1) process with additive outliers. Mathematics Subject Classification: 62M10, 91B84 2298 W. Panichkitkosolkul and S. Niwitpong