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On the Optimality of Adaptive Forecasting

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  • M. Nerlove

    (Econometric Institute, Rotterdam)

  • S. Wage

    (Econometric Institute, Rotterdam)

Abstract

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.

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File URL: http://dx.doi.org/10.1287/mnsc.10.2.207
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 10 (1964)
Issue (Month): 2 (January)
Pages: 207-224

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Handle: RePEc:inm:ormnsc:v:10:y:1964:i:2:p:207-224

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Cited by:
  1. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-548 National Bureau of Economic Research, Inc.
  2. Jacobs, Rodney L & Jones, Robert A, 1980. "The Treasury-Bill Futures Market," Journal of Political Economy, University of Chicago Press, vol. 88(4), pages 699-721, August.
  3. Rodney L. Jacobs & Robert A. Jones, 1978. "Price Expectations in the United States: 1947-1973," UCLA Economics Working Papers 107, UCLA Department of Economics.
  4. Francis X. Diebold & Lutz Kilian & Marc Nerlove, 2006. "Time Series Analysis," PIER Working Paper Archive 06-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    • Diebold, F.X. & Kilian, L. & Nerlove, Marc, 2006. "Time Series Analysis," Working Papers 28556, University of Maryland, Department of Agricultural and Resource Economics.
  5. Michael R. Darby, 1974. "Rational Expectations Under Conditions of Costly Information," UCLA Economics Working Papers 045, UCLA Department of Economics.
  6. Shepherd, Ben, 2012. "When are adaptive expectations rational? A generalization," Economics Letters, Elsevier, vol. 115(1), pages 4-6.
  7. Rodney L. Jacobs, 1978. "An Examination of the Economic and Muthian Rationality of Price Level Forecasts," UCLA Economics Working Papers 135A, UCLA Department of Economics.
  8. Rodney L. Jacobs & Robert A. Jones, 1977. "A Bayesian Approach to Adaptive Expectations," UCLA Economics Working Papers 093, UCLA Department of Economics.
  9. Victor Zarnowitz, 1982. "Expectations and Forecasts from Business Outlook Surveys," NBER Working Papers 0845, National Bureau of Economic Research, Inc.

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