A comparison of Box-Jenkins time series models with autoregressive processes

The idea of using a finite autoregressive (AR) process in conjunction with a Kalman filter, rather than a Box-Jenkins autoregressive moving-average (ARMA) model, to forecast a univariate time series is explored in the context of recursive estimation. It is shown through simulation that the AR representation yields a mean-square error (MSE) of prediction that is comparable to the nonlinear ARMA models. The parameter updating for the AR representation, however, is computationally very simple, whereas the Box-Jenkins method requires all calculations to be repeated when a new piece of data arrives. It is concluded that the simplicity of updating more than compensates for the increase in the MSE of prediction when one is faced with routinely forecasting a large number of variables.