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Predictive likelihood for Bayesian model selection and averaging

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  • Ando, Tomohiro
  • Tsay, Ruey
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    Abstract

    This paper investigates the performance of the predictive distributions of Bayesian models. To overcome the difficulty of evaluating the predictive likelihood, we introduce the concept of expected log-predictive likelihoods for Bayesian models, and propose an estimator of the expected log-predictive likelihood. The estimator is derived by correcting the asymptotic bias of the log-likelihood of the predictive distribution as an estimate of its expected value. We investigate the relationship between the proposed criterion and the traditional information criteria and show that the proposed criterion is a natural extension of the traditional ones. A new model selection criterion and a new model averaging method are then developed, with the weights for the individual models being dependent on their expected log-predictive likelihoods. We examine the performance of the proposed method using Monte Carlo experiments and a real example, which concerns the prediction of quarterly growth rates of real gross domestic product in the G7 countries. Out-of-sample forecasts show that the proposed methodology outperforms other methods available in the literature.

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    Bibliographic Info

    Article provided by Elsevier in its journal International Journal of Forecasting.

    Volume (Year): 26 (2010)
    Issue (Month): 4 (October)
    Pages: 744-763

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    Handle: RePEc:eee:intfor:v:26:y::i:4:p:744-763

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

    Related research

    Keywords: Model averaging Model selection Finance Predictive likelihood;

    References

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    1. James H. Stock & Mark W. Watson, 2001. "Forecasting output and inflation: the role of asset prices," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    2. Eklund, Jana & Karlsson, Sune, 2005. "Forecast Combination and Model Averaging Using Predictive Measures," CEPR Discussion Papers 5268, C.E.P.R. Discussion Papers.
    3. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    4. Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
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    6. Carmen Fernandez & E Ley & Mark F J Steel, 2004. "Benchmark priors for Bayesian models averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
    7. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    8. Gary Koop & Simon Potter, 2003. "Forecasting in Large Macroeconomic Panels using Bayesian Model Averaging," Discussion Papers in Economics 04/16, Department of Economics, University of Leicester.
    9. George Kapetanios & Vincent Labhard & Simon Price, 2006. "Forecasting Using Predictive Likelihood Model Averaging," Working Papers 567, Queen Mary, University of London, School of Economics and Finance.
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    12. Sadanori Konishi, 2004. "Bayesian information criteria and smoothing parameter selection in radial basis function networks," Biometrika, Biometrika Trust, vol. 91(1), pages 27-43, March.
    13. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    14. Zellner, Arnold, 2006. "S. James Press And Bayesian Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 10(05), pages 667-684, November.
    15. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
    16. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-62, April.
    17. Jose M. Perez, 2002. "Expected-posterior prior distributions for model selection," Biometrika, Biometrika Trust, vol. 89(3), pages 491-512, August.
    18. Tomohiro Ando, 2007. "Bayesian predictive information criterion for the evaluation of hierarchical Bayesian and empirical Bayes models," Biometrika, Biometrika Trust, vol. 94(2), pages 443-458.
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    Cited by:
    1. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.

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