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On the Optimality of Adaptive Forecasting

Author

Listed:
  • 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.

Suggested Citation

  • M. Nerlove & S. Wage, 1964. "On the Optimality of Adaptive Forecasting," Management Science, INFORMS, vol. 10(2), pages 207-224, January.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:2:p:207-224
    DOI: 10.1287/mnsc.10.2.207
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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 513-544, 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, 1978. "An Examination of the Economic and Muthian Rationality of Price Level Forecasts," UCLA Economics Working Papers 135A, UCLA Department of Economics.
    4. Bell, William Paul, 2009. "Adaptive interactive expectations: dynamically modelling profit expectations," MPRA Paper 38260, University Library of Munich, Germany, revised 09 Feb 2010.
    5. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    6. Bell, William Paul, 2008. "Adaptive Interactive Profit Expectations and Small World Networks," MPRA Paper 37924, University Library of Munich, Germany.
    7. 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.
    8. Jacob A. Mincer, 1969. "Models of Adaptive Forecasting," NBER Chapters, in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 83-111, National Bureau of Economic Research, Inc.
    9. Darby, Michael R, 1976. "Rational Expectations under Conditions of Costly Information," Journal of Finance, American Finance Association, vol. 31(3), pages 889-895, June.
    10. Shepherd, Ben, 2012. "When are adaptive expectations rational? A generalization," Economics Letters, Elsevier, vol. 115(1), pages 4-6.
    11. Gardner, Everette Jr., 2006. "Exponential smoothing: The state of the art--Part II," International Journal of Forecasting, Elsevier, vol. 22(4), pages 637-666.
    12. Rodney L. Jacobs & Robert A. Jones, 1978. "Price Expectations in the United States: 1947-1973," UCLA Economics Working Papers 107, UCLA Department of Economics.
    13. repec:pra:mprapa:37920 is not listed on IDEAS
    14. Roger F. Miller & Harold W. Watts, 1967. "A Model of Household Investment in Financial Assets," NBER Chapters, in: Determinants of Investment Behavior, pages 357-410, National Bureau of Economic Research, Inc.
    15. Rodney L. Jacobs & Robert A. Jones, 1977. "A Bayesian Approach to Adaptive Expectations," UCLA Economics Working Papers 093, UCLA Department of Economics.
    16. Victor Zarnowitz, 1982. "Expectations and Forecasts from Business Outlook Surveys," NBER Working Papers 0845, National Bureau of Economic Research, Inc.
    17. Kyriazi, Foteini & Thomakos, Dimitrios D. & Guerard, John B., 2019. "Adaptive learning forecasting, with applications in forecasting agricultural prices," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1356-1369.

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