Publication Type
Journal Article
Version
acceptedVersion
Publication Date
11-2018
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.
Keywords
Specification test, Point hypothesis test, Latent variable models, Markov chain Monte Carlo, Power enhancement technique, Information matrix
Discipline
Econometrics
Research Areas
Econometrics
Publication
Journal of Econometrics
Volume
207
Issue
1
First Page
237
Last Page
260
ISSN
0304-4076
Identifier
10.1016/j.jeconom.2018.08.001
Publisher
Elsevier: 24 months
Citation
LI, Yong; YU, Jun; and ZENG, Tao.
Specification tests based on MCMC output. (2018). Journal of Econometrics. 207, (1), 237-260.
Available at: https://ink.library.smu.edu.sg/soe_research/2220
Copyright Owner and License
Authors
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Additional URL
https://doi.org/10.1016/j.jeconom.2018.08.001