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WALS Prediction

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  • Magnus, J.R.
  • Wang, W.
  • Zhang, Xinyu

    (Tilburg University, Center for Economic Research)

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    Abstract

    Abstract: Prediction under model uncertainty is an important and difficult issue. Traditional prediction methods (such as pretesting) are based on model selection followed by prediction in the selected model, but the reported prediction and the reported prediction variance ignore the uncertainty from the selection procedure. This paper proposes a weighted average least squares (WALS) prediction procedure that is not conditional on the selected model. Taking both model and error uncertainty into account, we also propose an appropriate estimate of the variance of the WALS predictor. Correlations among the random errors are explicitly allowed. Compared to other prediction averaging methods, the WALS predictor has important advantages both theoretically and computationally. Simulation studies show that the WALS predictor generally produces lower mean squared prediction errors than its competitors, and that the proposed estimator for the prediction variance performs particularly well when model uncertainty increases.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2012-043.

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    Date of creation: 2012
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    Handle: RePEc:dgr:kubcen:2012043

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    Web page: http://center.uvt.nl

    Related research

    Keywords: Model averaging; Model uncertainty; Bayesian analysis; Prediction;

    This paper has been announced in the following NEP Reports:

    References

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    1. Jan R. Magnus & Dmitry Danilov, 2004. "Forecast accuracy after pretesting with an application to the stock market," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(4), pages 251-274.
    2. Wan, Alan T. K. & Zou, Guohua, 2003. "Optimal critical values of pre-tests when estimating the regression error variance: analytical findings under a general loss structure," Journal of Econometrics, Elsevier, vol. 114(1), pages 165-196, May.
    3. Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
    4. Jan R. Magnus, 2002. "Estimation of the mean of a univariate normal distribution with known variance," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 225-236, June.
    5. Jacobson, Tor & Karlsson, Sune, 2002. "Finding Good Predictors for Inflation: A Bayesian Model Averaging Approach," Working Paper Series 138, Sveriges Riksbank (Central Bank of Sweden).
    6. Wan, Alan T.K. & Zhang, Xinyu & Zou, Guohua, 2010. "Least squares model averaging by Mallows criterion," Journal of Econometrics, Elsevier, vol. 156(2), pages 277-283, June.
    7. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
    8. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644, September.
    9. Danilov, Dmitry & Magnus, J.R.Jan R., 2004. "On the harm that ignoring pretesting can cause," Journal of Econometrics, Elsevier, vol. 122(1), pages 27-46, September.
    10. Hilde C. Bjørnland & Karsten R. Gerdrup & Anne Sofie Jore & Leif Anders Thorsrud & Christie Smith, 2010. "Does forecast combination improve Norges Bank inflation forecasts?," Working Papers 0002, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    11. Ohtani, Kazuhiro & Toyoda, Toshihisa, 1980. "Estimation of regression coefficients after a preliminary test for homoscedasticity," Journal of Econometrics, Elsevier, vol. 12(2), pages 151-159, February.
    12. Yang, Yuhong, 2004. "Combining Forecasting Procedures: Some Theoretical Results," Econometric Theory, Cambridge University Press, vol. 20(01), pages 176-222, February.
    13. Aiolfi, Marco & Timmermann, Allan, 2006. "Persistence in forecasting performance and conditional combination strategies," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 31-53.
    14. Giles, Judith A & Giles, David E A, 1993. " Pre-test Estimation and Testing in Econometrics: Recent Developments," Journal of Economic Surveys, Wiley Blackwell, vol. 7(2), pages 145-97, June.
    15. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
    16. Toyoda, Toshihsa & Wallace, T D, 1976. "Optimal Critical Values for Pre-Testing in Regression," Econometrica, Econometric Society, vol. 44(2), pages 365-75, March.
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