The general procedure followed in the present paper is to show that, although the series generated by the Theil-Wage model [Theil, H., S. Wage. 1964. Some observations on adaptive forecasting. Management Sci. 10.] is nonstationary, there exists a simple transform of the series, in this case the second difference, which is stationary. This observation permits the Wiener-Hopf theory for stationary series to be applied to the transformed series. It is then shown that the results obtained by Theil and Wage are simply related to the optimal constant-parameter, linear predictors of the transformed series and thus that the adaptive forecasts are optimal in a rather wide sense. We believe, therefore, that the results of this paper illustrate a general approach to the prediction of non-stationary time series, and these are, after all, the type mainly encountered in economic or management problems. Thus the paper may have a somewhat wider significance than its title or primary purpose might suggest.
