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A new approach to Bayesian hypothesis testing

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  • Li, Yong
  • Zeng, Tao
  • Yu, Jun

Abstract

In this paper a new Bayesian approach is proposed to test a point null hypothesis based on the deviance in a decision-theoretical framework. The proposed test statistic may be regarded as the Bayesian version of the likelihood ratio test and appeals in practical applications with three desirable properties. First, it is immune to Jeffreys’ concern about the use of improper priors. Second, it avoids Jeffreys–Lindley’s paradox, Third, it is easy to compute and its threshold value is easily derived, facilitating the implementation in practice. The method is illustrated using some real examples in economics and finance. It is found that the leverage effect is insignificant in an exchange time series and that the Fama–French three-factor model is rejected.

Suggested Citation

  • Li, Yong & Zeng, Tao & Yu, Jun, 2014. "A new approach to Bayesian hypothesis testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 602-612.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:p3:p:602-612
    DOI: 10.1016/j.jeconom.2013.08.035
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    2. Yong Li & Xiaobin Liu & Jun Yu & Tao Zeng, 2018. "A New Wald Test for Hypothesis Testing Based on MCMC outputs," Papers 1801.00973, arXiv.org.
    3. Liu, Xiaobin & Li, Yong & Yu, Jun & Zeng, Tao, 2022. "Posterior-based Wald-type statistics for hypothesis testing," Journal of Econometrics, Elsevier, vol. 230(1), pages 83-113.
    4. Li, Yong & Liu, Xiao-Bin & Yu, Jun, 2015. "A Bayesian chi-squared test for hypothesis testing," Journal of Econometrics, Elsevier, vol. 189(1), pages 54-69.
    5. Xiao-Bin Liu & Yong Li, 2013. "Bayesian testing volatility persistence in stochastic volatility models with jumps," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1415-1426, December.
    6. Ronaldo Carpio & Meixin Guo, 2021. "Bayesian estimation of the Eurozone currency union effect," Review of International Economics, Wiley Blackwell, vol. 29(3), pages 511-532, August.
    7. Zhao, Yan-Yong & Lin, Jin-Guan & Xu, Pei-Rong & Ye, Xu-Guo, 2015. "Orthogonality-projection-based estimation for semi-varying coefficient models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 204-221.
    8. Yong Li & Jun Yu, 2019. "An Improved Bayesian Unit Root Test in Stochastic Volatility Models," Annals of Economics and Finance, Society for AEF, vol. 20(1), pages 103-122, May.
    9. Zhang, Yonghui & Chen, Zhongtian & Li, Yong, 2017. "Bayesian testing for short term interest rate models," Finance Research Letters, Elsevier, vol. 20(C), pages 146-152.
    10. Leung, Melvern & Li, Youwei & Pantelous, Athanasios A. & Vigne, Samuel A., 2021. "Bayesian Value-at-Risk backtesting: The case of annuity pricing," European Journal of Operational Research, Elsevier, vol. 293(2), pages 786-801.
    11. Chen, Shyh-Wei & Hsu, Chi-Sheng & Xie, Zixong, 2016. "Are there periodically collapsing bubbles in the stock markets? New international evidence," Economic Modelling, Elsevier, vol. 52(PB), pages 442-451.
    12. Doğan, Osman & Taşpınar, Süleyman & Bera, Anil K., 2021. "A Bayesian robust chi-squared test for testing simple hypotheses," Journal of Econometrics, Elsevier, vol. 222(2), pages 933-958.
    13. Cross, Jamie L. & Hou, Chenghan & Trinh, Kelly, 2021. "Returns, volatility and the cryptocurrency bubble of 2017–18," Economic Modelling, Elsevier, vol. 104(C).
    14. Jin-Yu Zhang & Zhong-Tian Chen & Yong Li, 2019. "Bayesian Testing for Leverage Effect in Stochastic Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 1153-1164, March.
    15. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "International Financial Markets," Post-Print halshs-02183053, HAL.

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    More about this item

    Keywords

    Bayes factor; Decision theory; EM algorithm; Deviance; Markov chain Monte Carlo; Latent variable models;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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