Noninformative priors and frequentist risks of bayesian estimators of vector-autoregressive models

In this study, we examine posterior properties and frequentist risks of Bayesian estimators based on several noninformative priors in vector autoregressive (VAR) models. We prove existence of the posterior distributions and posterior moments under a general class of priors. Using a variety of priors in this class we conduct numerical simulations of posteriors. We find that in most examples Bayesian estimators with a shrinkage prior on the VAR coefficients and the reference prior of Yang and Berger (Ann. Statist. 22 (1994) 1195) on the VAR covariance matrix dominate MLE, Bayesian estimators with the diffuse prior, and Bayesian estimators with the prior used in RATS. We also examine the informative Minnesota prior and find that its performance depends on the nature of the data sample and on the tightness of the Minnesota prior. A tightly set Minnesota prior is better when the data generating processes are similar to random walks, but the shrinkage prior or constant prior can be better otherwise.