10 - Hypothesis Testing Statistics Based on Posterior Output with Applications in Financial Econometrics

Summary

This chapter overviews three recently developed posterior test statistics for hypothesis testing based on posterior output. These three statistics can be viewed as the posterior version of the trinity of test statistics based on maximum likelihood (ML), namely, the likelihood ratio (LR) test, the Lagrange multiplier (LM) test, and the Wald test. The asymptotic distributions of the test statistics are discussed under repeated sampling. Furthermore, based on the Bernstein–von Mises theorem, the equivalence of the confidence interval construction between the set of posterior tests and their frequentist counterparts is developed, giving the posterior tests a frequentist asymptotic justification. The three statistics are applicable to many popular financial econometric models, including asset pricing models,copula models, and so on. Studies based on simulated data and real data in the context of several financial econometric models are carried out to illustrate the finite sample behavior and the usefulness of the test statistics.