Bayesian analysis of vector autoregressions

Lars Sune Karlsson, Purdue University

Abstract

This thesis investigates various methods of generalizing the Bayesian Analysis of Vector Autoregressions due to Litterman. Specifically, prior-posterior pairs which allow for dependence between the equations of the Vector Autoregression are considered. The various methods are evaluated based on their forecast performance. Since the posterior distribution of the forecasts are intractable for several of the priors considered, numerical methods are used to evaluate the posterior moments of the forecasts. The numerical method used is Monte Carlo integration with importance sampling and antithetic variates. The kernel of the 2-0 poly t probability density function is introduced as an importance function for densities that are expressed as products of two densities. This importance function is successfully applied to the posterior arising from a Normal-Diffuse prior. The use of antithetic variates reduce the computational effort by between 50% and 99.8%. It is found that, except, for situations where the likelihood function dominates the posterior distribution, the Bayesian methods produce better forecasts than Vector Autoregressions estimated by OLS. The generalized methods generally perform better than the so called Minnesota prior of Litterman.

Degree

Ph.D.

Advisors

Kadiyala, Purdue University.

Subject Area

Economics

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