The decomposition of forecast in seasonal ARIMA models

This paper presents a procedure to break down the forecast function of a seasonal ARIMA model in terms of its permanent and transitory components. Both depend on the initial values at the forecast origin, but their structures are fixed and independent of this origin. The permanent component is an estimate of the long-run projection of the corresponding economic variable and the transitory element describes the approach towards the permanent one. Within the permanent component a distinction is made between the factors that depend on the initial conditions of the system and those that are deterministic. The procedure is compared to other methods presented in the literature and illustrated in an example.