ARIMA-GARCH and unobserved component models with GARCH disturbances: Are their prediction intervals different?∗

We analyze the effects on prediction intervals of fitting ARIMA models to series with stochastic trends, when the underlying components are heteroscedastic. We show that ARIMA prediction intervals may be inadequate when only the transitory component is heteroscedastic. In this case, prediction intervals based on the unobserved component models tend to the homoscedastic intervals as the prediction horizon increases. However, prediction intervals based on the ARIMA model incorporate the unit root, so they diverge for ever from the homoscedastic intervals. We focus on the local level and smooth trend models. All the results are illustrated with simulated and real time series.