A Specification Test based on the MCMC Output

Yong Li (), Jun Yu and Tao Zeng ()
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Yong Li: Hanqing Advanced Institute of Economics and Finance, Renmin University of China
Tao Zeng: Department of Finance, Wuhan University

No 9-2017, Economics and Statistics Working Papers from Singapore Management University, School of Economics

Abstract: A test statistic is proposed to assess the model specification after the model is estimated by Bayesian MCMC methods. The new test is motivated from the power enhancement technique of Fan, Liao and Yao (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 null model. 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 X2-distributed, suggesting that the proposed test is asymptotically pivotal, when the null model is correctly specified. The proposed test has several properties. First, its size distortion is small and hence bootstrap methods can be avoided. Second, it is easy to compute from the 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 specification of the null model and J1 takes a large value, the test suggests the source of misspecification of the null model. 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.

Keywords: Specification test; Point hypothesis test; Latent variable models; Markov chain Monte Carlo; Power enhancement technique; Information matrix (search for similar items in EconPapers)
JEL-codes: C11 C12 G12 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2017-05-10
New Economics Papers: this item is included in nep-ecm and nep-ore
Note: Paper available on: http://ink.library.smu.edu.sg/soe_research/1967/
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Journal Article: Specification tests based on MCMC output (2018)
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