Large Sample Properties of Posterior Densities, Bayesian Information Criterion and the Likelihood Principle in Nonstationary Time Series Models

Asymptotic normality of posterior is a well understood result for dynamic as well as non-dynamic models based on sets of abstract conditions that are hard to verify especially for the case of nonstationarity. In this paper the authors provide a set of conditions by which they can relatively easily prove the asymptotic posterior normality under quite general situations of possible nonstationarity. This result reinforces and generalizes the validity of inference based on the likelihood principle. On the other hand, the authors' conditions allow them to generalize Bayesian decision criterion to the case of possible nonstationarity. In addition, the authors have shown that consistency of the maximum likelihood estimator, not the asymptotic normality of the estimator, with some minor additional assumptions is sufficient for the asymptotic posterior normality.