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Least-squares forecast averaging

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  • Hansen, Bruce E.

Abstract

This paper proposes forecast combination based on the method of Mallows Model Averaging (MMA). The method selects forecast weights by minimizing a Mallows criterion. This criterion is an asymptotically unbiased estimate of both the in-sample mean-squared error (MSE) and the out-of-sample one-step-ahead mean-squared forecast error (MSFE). Furthermore, the MMA weights are asymptotically mean-square optimal in the absence of time-series dependence. We show how to compute MMA weights in forecasting settings, and investigate the performance of the method in simple but illustrative simulation environments. We find that the MMA forecasts have low MSFE and have much lower maximum regret than other feasible forecasting methods, including equal weighting, BIC selection, weighted BIC, AIC selection, weighted AIC, Bates-Granger combination, predictive least squares, and Granger-Ramanathan combination.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 146 (2008)
Issue (Month): 2 (October)
Pages: 342-350

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Handle: RePEc:eee:econom:v:146:y:2008:i:2:p:342-350

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Mallows AIC BIC BMA Forecast combination Model selection;

References

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  1. Carmen Fernandez & Eduardo Ley & Mark F.J. Steel, 1998. "Benchmark Priors for Bayesian Model Averaging," Econometrics 9804001, EconWPA, revised 31 Jul 1999.
  2. Marco Aiolfi & Carlos Capistrán & Allan Timmermann, 2010. "Forecast Combinations," CREATES Research Papers 2010-21, School of Economics and Management, University of Aarhus.
  3. Wright, Jonathan H., 2008. "Bayesian Model Averaging and exchange rate forecasts," Journal of Econometrics, Elsevier, vol. 146(2), pages 329-341, October.
  4. Gernot Doppelhofer & Ronald I. Miller & Xavier Sala-i-Martin, 2000. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," NBER Working Papers 7750, National Bureau of Economic Research, Inc.
  5. Francis X. Diebold & Jose A. Lopez, 1996. "Forecast Evaluation and Combination," NBER Technical Working Papers 0192, National Bureau of Economic Research, Inc.
  6. Stock, James H. & Watson, Mark W., 2006. "Forecasting with Many Predictors," Handbook of Economic Forecasting, Elsevier.
  7. Min, C.K. & Zellner, A., 1992. ""Bayesian and Non-Bayesian Methods for Combining Models and Forecasts with Applications to Forecasting International Growth Rates"," Papers 90-92-23, California Irvine - School of Social Sciences.
  8. Mark W. Watson & James H. Stock, 2004. "Combination forecasts of output growth in a seven-country data set," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 405-430.
  9. Hjort N.L. & Claeskens G., 2003. "Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 879-899, January.
  10. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
  11. Carmen Fernandez & Eduardo Ley & Mark Steel, 1999. "Model uncertainty in cross-country growth regressions," Econometrics 9903003, EconWPA, revised 06 Oct 2001.
  12. Avramov, Doron, 2002. "Stock return predictability and model uncertainty," Journal of Financial Economics, Elsevier, vol. 64(3), pages 423-458, June.
  13. Jonathan H. Wright, 2009. "Forecasting US inflation by Bayesian model averaging," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(2), pages 131-144.
  14. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
  15. Ing, Ching-Kang & Wei, Ching-Zong, 2003. "On same-realization prediction in an infinite-order autoregressive process," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 130-155, April.
  16. R. Bhansali, 1996. "Asymptotically efficient autoregressive model selection for multistep prediction," Annals of the Institute of Statistical Mathematics, Springer, vol. 48(3), pages 577-602, September.
  17. Ing, Ching-Kang, 2003. "Multistep Prediction In Autoregressive Processes," Econometric Theory, Cambridge University Press, vol. 19(02), pages 254-279, April.
  18. Ching-Kang Ing, 2005. "Accumulated Prediction Errors, Information Criteria And Optimal Forecasting For Autoregressive Time Series," Econometrics 0503020, EconWPA.
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