Prediction intervals for ARIMA models

The problem of constructing prediction intervals for linear time series (AR IMA) models is examined. The aim is to find prediction intervals that incor porate an allowance for sampling error associated with parameter estimates. The effect of constraints on parameters arising from stationarity and inve rtibility conditions is also incorporated. Two new methods, based on varyin g degrees of first-order Taylor approximations, are proposed. These are com pared in a simulation study to two existing methods, a heuristic approach a nd the "plug-in" method whereby parameter values are set equal to their max imum likelihood estimates. A comparison of the four methods is also made fo r quarterly retail sales for 10 Organization for Economic Cooperation and D evelopment countries. The new approaches provide a systematic improvement o ver existing methods.