Prediction Intervals for an Unknown Mean Gaussian Autoregressive Process Using the Residual Model

Abstract

This paper presents a new one-step-ahead prediction interval for an unknown mean Gaussian autoregressive process (AR(p)) using the residual model. The proposed prediction interval is constructed by adding the multiplication of the correction factor and the percentile of sample errors in the estimated point forecast for an AR(p) process. The coverage probabilities of a new prediction interval and a standard prediction interval are also derived to be functionally independent of the population mean and the variance of the innovation process. TheMonte Carlosimulation is used to investigate the behavior of this new prediction interval compared to the existing prediction interval based on their coverage probabilities and expected lengths. Simulation results have shown that almost cases of the new prediction interval have desired minimum coverage probabilities of 0.95 and 0.90. Moreover, this new one is better than a standard prediction interval for all the autoregressive parameter values and all sample sizes considered in this paper.