A Bayesian Specification Test

A Bayesian test statistic is proposed to assess the model specification after the model is estimated by Bayesian MCMC methods. The proposed approach does not require an alternative model to be specified and is applicable to a variety of models, including latent variable models for which frequentist methods are difficult to use. The properties of the test statistic are established and its implementation is discussed. The test is easy to use and the test statistic can be calculated from MCMC outputs even when there are latent variables. The finite sample properties are investigated using simulated data. The method is illustrated in a linear regression model, a dynamic factor model, and a stochastic volatility model using real data.

JEL Classification: C11, C12, G12

Keywords: EM algorithm; Specification test; Latent variable models; Markov chain Monte Carlo; Dynamic factor; Stochastic volatility

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