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A Bayesian chi-squared test for hypothesis testing

Author

Listed:
  • Li, Yong
  • Liu, Xiao-Bin
  • Yu, Jun
Abstract
A new Bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss. The proposed test statistic may be regarded as the Bayesian version of the Lagrange multiplier test. Its asymptotic distribution is obtained based on a set of regular conditions and follows a chi-squared distribution when the null hypothesis is correct. The new statistic has several important advantages that make it appealing in practical applications. First, it is well-defined under improper prior distributions. Second, it avoids Jeffrey–Lindley’s paradox. Third, it always takes a non-negative value and is relatively easy to compute, even for models with latent variables. Fourth, its numerical standard error is relatively easy to obtain. Finally, it is asymptotically pivotal and its threshold values can be obtained from the chi-squared distribution. The method is illustrated using some real examples in economics and finance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:189:y:2015:i:1:p:54-69
    DOI: 10.1016/j.jeconom.2015.06.021
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    Cited by:

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    3. Baruník, Jozef & Ellington, Michael, 2024. "Persistence in financial connectedness and systemic risk," European Journal of Operational Research, Elsevier, vol. 314(1), pages 393-407.
    4. Li, Yong & Yu, Jun & Zeng, Tao, 2018. "Specification tests based on MCMC output," Journal of Econometrics, Elsevier, vol. 207(1), pages 237-260.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Cross, Jamie L. & Hou, Chenghan & Trinh, Kelly, 2021. "Returns, volatility and the cryptocurrency bubble of 2017–18," Economic Modelling, Elsevier, vol. 104(C).
    11. 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.
    12. Guanhao Feng & Jingyu He, 2019. "Factor Investing: A Bayesian Hierarchical Approach," Papers 1902.01015, arXiv.org, revised Sep 2020.

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    More about this item

    Keywords

    Bayes factor; Decision theory; EM algorithm; Lagrange multiplier; 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

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