# Specification tests based on MCMC output

*Yong Li*,
*Jun Yu* () and
*Tao Zeng*

*Journal of Econometrics*, 2018, vol. 207, issue 1, 237-260

**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 (search for similar items in EconPapers)

**JEL-codes:** C11 C12 G12 (search for similar items in EconPapers)

**Date:** 2018

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** Track citations by RSS feed

**Downloads:** (external link)

http://www.sciencedirect.com/science/article/pii/S0304407618301416

Full text for ScienceDirect subscribers only

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:eee:econom:v:207:y:2018:i:1:p:237-260

Access Statistics for this article

Journal of Econometrics is currently edited by *T. Amemiya*, *A. R. Gallant*, *J. F. Geweke*, *C. Hsiao* and *P. M. Robinson*

More articles in Journal of Econometrics from Elsevier

Bibliographic data for series maintained by Dana Niculescu ().