Bayesian estimates for vector autoregressive models

This article examines frequentist risks of Bayesian estimates of vector autoregressive (VAR) regression coefficient and error covariance matrices under competing loss functions, under various noninformative priors, and in the normal and Student-t models. Simulation results show that for the regression coefficient matrix, an asymmetric LINEX estimator does better overall than the posterior mean. No dominating estimator emerges for the error covariance matrix. We find that the choice of prior has a more significant effect on the estimates than the form of estimator. For the VAR regression coefficients, a shrinkage prior dominates a constant prior. For the error covariance matrix, Yang and Berger's reference prior dominates the Jeffreys prior. Estimation of a VAR using U.S. macroeconomic data yields significantly different estimates under competing priors.