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Specification tests based on MCMC output

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

Abstract

Two test statistics are proposed to determine model specification after a model is estimated by an MCMC method. The first test is the MCMC version of IOSA test and its asymptotic null distribution is normal. The second test is motivated from the power enhancement technique of Fan et al. (2015). It combines a component (J1) that tests a null point hypothesis in an expanded model and a power enhancement component (J0) obtained from the first test. It is shown that J0 converges to zero when the null model is correctly specified and diverges when the null model is misspecified. Also shown is that J1 is asymptotically χ2-distributed, suggesting that the second test is asymptotically pivotal, when the null model is correctly specified. The main feature of the first test is that no alternative model is needed. The second test has several properties. First, its size distortion is small and hence bootstrap methods can be avoided. Second, it is easy to compute from MCMC output and hence is applicable to a wide range of models, including latent variable models for which frequentist methods are difficult to use. Third, when the test statistic rejects the null model and J1 takes a large value, the test suggests the source of misspecification. The finite sample performance is investigated using simulated data. The method is illustrated in a linear regression model, a linear state-space model, and a stochastic volatility model using real data.

Suggested Citation

  • Li, Yong & Yu, Jun & Zeng, Tao, 2018. "Specification tests based on MCMC output," Journal of Econometrics, Elsevier, vol. 207(1), pages 237-260.
    • Handle: RePEc:eee:econom:v:207:y:2018:i:1:p:237-260
    DOI: 10.1016/j.jeconom.2018.08.001
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    More about this item

    Keywords

    Specification test; Point hypothesis test; Latent variable models; Markov chain Monte Carlo; Power enhancement technique; Information matrix;
    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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