A specification test based on the MCMC output

• Main Authors: LI, Yong, YU, Jun, ZENG, Tao
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2017
• Subjects: Specification test; Point hypothesis test; Latent variable models; Markov chain Monte Carlo; Power enhancement technique; Information matrix; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/1967; https://ink.library.smu.edu.sg/context/soe_research/article/2966/viewcontent/BTSpecification55_.pdf
• Institution: Singapore Management University

A test statistic is proposed to assess themodel specification after the model is estimated by Bayesian MCMC methods. Thenew test is motivated from the power enhancement technique of Fan, Liao and Yao(2015). It combines a component (J1) that tests anull 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 anddiverges when the null model is misspecified. Also shown is that J1 is asymptotically X2-distributed, suggesting that theproposed test is asymptotically pivotal, when the null model is correctlyspecified. The proposed test has several properties. First, its size distortionis small and hence bootstrap methods can be avoided. Second, it is easy tocompute from the MCMC output and hence is applicable to a wide range of models,including latent variable models for which frequentist methods are difficult touse. Third, when the test statistic rejects the specification of the null modeland J1 takes a large value, thetest suggests the source of misspecification of the null model. The finitesample performance is investigated using simulated data. The method isillustrated in a linear regression model, a linear state-space model, and astochastic volatility model using real data.