The problem of constructing prediction intervals for linear time series (ARIMA) models is examined. The aim is to find prediction intervals which incorporate an allowance for sampling error associated with parameter estimates. The effect of constraints on parameters arising from stationarity and invertibility conditions is also incorporated. Two new methods, based to varying degrees on first-order Taylor approximations, are proposed. These are compared in a simulation study to two existing methods: a heuristic approach and the `plug-in' method whereby parameter values are set equal to their maximum likelihood estimates