On Coverage Probability of a Prediction Interval for an Unknown Mean AR(1) Process Using Combined Predictors

Abstract

A new prediction interval for an unknown mean first-order autoregressive process (AR(1)) using combined predictors from a stationary process and a non stationary process is investigated in this paper. 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. Monte Carlo simulation shows that a new prediction interval has a desired minimum coverage probability 1−α, which is better than a standard prediction interval for all the autoregressive parameter values used and for all sample sizes considered in this paper.