One-sided simultaneous prediction intervals for AR(1) and MA(1) processes with exponential innovations

This paper is concerned with the determination of simultaneous confidence regions for some types of time series models. It derives recursive formulas which allow the determination of the probability for an AR(1) stationary process based on exponential inputs to lie under any sequence of constants during N steps. Also, probabilities of the same form are derived for an MA(1) process, based on an exponentially distributed white noise. Numerical results are obtained and comparison of prediction regions for different values of φ or θ is made. The results show how the use of the correlation structure of the models can reduce the confidence regions' area.