The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Prediction Formulas

  • Charles H. Whiteman
  • Kurt F. Lewis
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2180

Abstract

Prediction formulas for multi-step forecasts and geometric distributed leads of stationary time series are derived using classical, frequency domain methods. Starting with the Wold representation, optimal squared-error loss predictions are derived using the analytic function theory approach of Whittle. This approach is easily adapted to the problem of making predictions that are robust under model misspecification. Forecasts and expected present value calculations are illustrated under both objectives for low-order autoregressive and moving average processes.

Keywords

Blaschke factors Contour integral Cross-equation restrictions Distributed leads Frequency domain problems Least squares Linear least squares projection Minimum norm interpolation problem Min-max problem Misspecification Prediction formulas Rational expectations Riesz–Fisher th Robustness Squared-error loss optimal prediction Time domain problems Wiener–Hopf equation Wold decomposition th Wold representation 

JEL Classifications

C1 
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Bibliography

  1. Hansen, L.P., and T.J. Sargent. 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 T.J. Sargent. 2007. Robustness. Princeton: Princeton University Press.Google Scholar
  3. Kasa, K. 2001. A robust Hansen–Sargent prediction formula. Economic Letters 71: 43–48.CrossRefGoogle Scholar
  4. Nehari, Z. 1957. On bounded bilinear forms. Annals of Mathematics 65(1): 153–162.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 ed. Minneapolis: University of Minnesota Press.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Charles H. Whiteman
    • 1
  • Kurt F. Lewis
    • 1
  1. 1.