Prediction formulas

Abstract

This article reviews the derivation of formulas for linear least squares and robust prediction of stationary time series and geometrically discounted distributed leads of such series. The derivations employed are the classical, frequency-domain procedures employed by Whittle (1983) and Whiteman (1983), and result in nearly closed-form expressions. The formulas themselves are useful directly in forecasting, and have also found uses in economic modelling, primarily in macroeconomics. Indeed, Hansen and Sargent (1980) refer to the cross-equation restrictions connecting the time series representation of driving variables to the analogous representation for predicting the present value of such variables as the ‘hallmark of rational expectations models’.