Prediction Formulas

  • Charles H. Whiteman
  • Kurt F. Lewis
Reference work entry


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’.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Hansen, L.P. and Sargent, T.J. (1980). Formulating and estimating dynamic linear rational expectations models. Journal of Economic Dynamics and Control 2, 7–46.CrossRefGoogle Scholar
  2. Hansen, L.P. and Sargent, T.J. (2007) Robustness. (Princeton: Princeton University Press).Google Scholar
  3. Kasa, K. (2001). A robust Hansen-Sargent prediction formula. Economic Letters 71, 43–8.CrossRefGoogle Scholar
  4. Nehari, Z. 1957. On bounded bilinear forms. Annals of Mathematics 65(1), 153–62.CrossRefGoogle Scholar
  5. Sargent, T.J. (1987) Macroeconomic Theory. (New York: Academic Press).Google Scholar
  6. Whiteman, C.H. (1983) Linear Rational Expectations: A User’s Guide. (Minneapolis: University of Minnesota Press).Google Scholar
  7. Whittle, P. 1983. Prediction and Regulation by Linear Least-square Methods, 2nd edn. Minneapolis: University of Minnesota Press.Google Scholar

Copyright information

© Palgrave Macmillan, a division of Macmillan Publishers Limited 2008

Authors and Affiliations

  • Charles H. Whiteman
  • Kurt F. Lewis

There are no affiliations available

Personalised recommendations