IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

Predictive likelihood for Bayesian model selection and averaging

  • Ando, Tomohiro
  • Tsay, Ruey
Registered author(s):

    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.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

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

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

    in new window

    Handle: RePEc:eee:intfor:v:26:y::i:4:p:744-763
    Contact details of provider: Web page:

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    as in new window
    1. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    2. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    3. James H. Stock & Mark W. Watson, 1999. "Forecasting Inflation," NBER Working Papers 7023, National Bureau of Economic Research, Inc.
    4. Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
    5. James H. Stock & Mark W. Watson, 2001. "Forecasting Output and Inflation: The Role of Asset Prices," NBER Working Papers 8180, National Bureau of Economic Research, Inc.
    6. 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.
    7. 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.
    8. Mario Forni & Marc Hallin & Lucrezia Reichlin & Marco Lippi, 2000. "The generalised dynamic factor model: identification and estimation," ULB Institutional Repository 2013/10143, ULB -- Universite Libre de Bruxelles.
    9. 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.
    10. Eklund, Jana & Karlsson, Sune, 2005. "Forecast Combination and Model Averaging Using Predictive Measures," CEPR Discussion Papers 5268, C.E.P.R. Discussion Papers.
    11. Gary Koop & Simon M. Potter, 2003. "Forecasting in large macroeconomic panels using Bayesian Model Averaging," Staff Reports 163, Federal Reserve Bank of New York.
    12. 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.
    13. Zellner, Arnold, 2006. "S. James Press And Bayesian Analysis," Macroeconomic Dynamics, Cambridge University Press, vol. 10(05), pages 667-684, November.
    14. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    15. Hansen, Bruce E., 2008. "Least-squares forecast averaging," Journal of Econometrics, Elsevier, vol. 146(2), pages 342-350, October.
    16. 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.
    17. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    18. Jose M. Perez, 2002. "Expected-posterior prior distributions for model selection," Biometrika, Biometrika Trust, vol. 89(3), pages 491-512, August.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:intfor:v:26:y::i:4:p:744-763. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.