Autoregressive model selection for multistep prediction

A direct method for multistep prediction of a stationary time series consists of fitting a new autoregression for each lead time, h, by a linear regression procedure and to select the order to be fitted from the data. By contrast, a more usual 'plug-in' method involves the least-squares fitting of an initial kth-order autoregression; the multistep forecasts are then obtained from the model equation, but with the unknown future values replaced by their own forecasts. A derivation of the h-step final prediction error, FPE, criterion to be used in conjunction with the direct method is given. A lead-time-dependent procedure for order selection when using the plug-in method is also examined and it is shown not to have satisfactory asymptotic properties. The finite sample behaviour of the order selected by the direct method is investigated by a simulation study. (C) 1999 Elsevier Science B.V. All rights reserved.