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Bayesian Averaging, Prediction and Nonnested Model Selection

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  • Han Hong
  • Bruce Preston

Abstract

This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models.

Suggested Citation

  • Han Hong & Bruce Preston, 2008. "Bayesian Averaging, Prediction and Nonnested Model Selection," NBER Working Papers 14284, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:14284
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    Cited by:

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    2. Huigang Chen & Mr. Alin T Mirestean & Mr. Charalambos G Tsangarides, 2011. "Limited Information Bayesian Model Averaging for Dynamic Panels with An Application to a Trade Gravity Model," IMF Working Papers 2011/230, International Monetary Fund.
    3. Erhard Reschenhofer & David Preinerstorfer & Lukas Steinberger, 2013. "Non-monotonic penalizing for the number of structural breaks," Computational Statistics, Springer, vol. 28(6), pages 2585-2598, December.
    4. Eric Hillebrand & Marcelo C. Medeiros, 2016. "Nonlinearity, Breaks, and Long-Range Dependence in Time-Series Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 23-41, January.
    5. Carlos Carvalho & Stefano Eusepi & Emanuel Moench & Bruce Preston, 2023. "Anchored Inflation Expectations," American Economic Journal: Macroeconomics, American Economic Association, vol. 15(1), pages 1-47, January.
    6. Mao, Guangyu, 2015. "Model selection of M-estimation models using least squares approximation," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 238-243.
    7. Alexander Vosseler & Enzo Weber, 2018. "Forecasting seasonal time series data: a Bayesian model averaging approach," Computational Statistics, Springer, vol. 33(4), pages 1733-1765, December.
    8. Mao, Guangyu, 2013. "Model selection for regression with heteroskedastic and autocorrelated errors," Economics Letters, Elsevier, vol. 118(3), pages 497-501.
    9. Koetter, Michael & Poghosyan, Tigran, 2010. "Real estate prices and bank stability," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1129-1138, June.
    10. Cui, Xiaomeng & Gafarov, Bulat & Ghanem, Dalia & Kuffner, Todd, 2024. "On model selection criteria for climate change impact studies," Journal of Econometrics, Elsevier, vol. 239(1).
    11. Li, Cheng & Jiang, Wenxin, 2016. "On oracle property and asymptotic validity of Bayesian generalized method of moments," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 132-147.
    12. Siddharta Chib & Minchul Shin & Anna Simoni, 2016. "Bayesian Empirical Likelihood Estimation and Comparison of Moment Condition Models," Working Papers 2016-21, Center for Research in Economics and Statistics.
    13. Minerva Mukhopadhyay & Sourabh Bhattacharya, 2022. "Bayes factor asymptotics for variable selection in the Gaussian process framework," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 581-613, June.
    14. Mr. Alin T Mirestean & Mr. Charalambos G Tsangarides & Huigang Chen, 2009. "Limited Information Bayesian Model Averaging for Dynamic Panels with Short Time Periods," IMF Working Papers 2009/074, International Monetary Fund.
    15. Barbaglia, Luca & Frattarolo, Lorenzo & Onorante, Luca & Pericoli, Filippo Maria & Ratto, Marco & Tiozzo Pezzoli, Luca, 2023. "Testing big data in a big crisis: Nowcasting under Covid-19," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1548-1563.
    16. Brück, Florian & Fermanian, Jean-David & Min, Aleksey, 2023. "A corrected Clarke test for model selection and beyond," Journal of Econometrics, Elsevier, vol. 235(1), pages 105-132.
    17. Javier García-Cicco & Roque Montero, 2011. "Modeling Copper Price: A Regime-Switching Approach," Working Papers Central Bank of Chile 613, Central Bank of Chile.
    18. Kira Alhorn & Holger Dette & Kirsten Schorning, 2021. "Optimal Designs for Model Averaging in non-nested Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 745-778, August.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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