Updating the forecast function of ARIMA models and the link with DLMs

This paper shows that the whole forecast function of ARIMA time series models, and not just the eventual forecast function, may be updated each time an observation is received. The paper also shows that the coefficients in the updating equations for the forecast function may be expressed in exactly the same form as the Kalman filter updating equations for canonical time series DLMs. Moreover, the adaptive factors in the updating equations are shown to be a simple function of the ARIMA model parameters.