Bayesian Vector Autoregressive Analysis

Abstract

The dissertation investigates various aspects of Bayesian inference in time series econometrics. It consists of one expository chapter and two research papers. The first chapter presents on an easy example of a production function for the USA the development of Bayesian models in the context of time series analysis. The model analysed is the Cobb-Douglas production function with covariance stationary AR(1) disturbances. The methods presented are used extensively in the next two chapters. The first research paper tackles the issue of identifiation in a SVAR model with an error term being a Markov mixture of normal distributions. Non-Gaussianity can be employed for the identification of shocks. So far only classical methods have been proposed for this class of models. Bayesian methods for inference are presented, in particular an efficient method for testing homogeneity of shock process. An empirical example presents the workings of the tools developed. The topic of the second paper is the forecasting with Bayesian VARs. Owing to the shrinkage, the original Minnesota prior was reported to provide significant improvements in forecasting accuracy. Its limitations however, gave rise to research trying to relax restrictive treatment of the residual covariance matrix, and to allow for the possibility of cointegration in the system. This paper first disentangles in a unified framework and a balanced environment of optimizing choice of hyperparameters the impact on the predictive power of BVARs of developments of priors along the above two dimensions; a well known historical dataset is analyzed for this purpose. As the second contribution, the paper presents a novel prior characterized by explicit modelling of cointegration that avoids certain unattractive restrictive properties of the previously used priors; the potential of the prior for elicitation from the well established Litterman beliefs is demonstrated as well as predictive accuracy improvements over the benchmarks.