Cointegration concerns at least two time series which
individually drift extensively, but which cannot wander too far away from
each other. This simple concept has caused what is perhaps best described
as a revolution in empirical macroeconomics.
This thesis is devoted to a Bayesian analysis of cointegration in vector autoregressive processes. Four included papers treat various important aspects of cointegration, e. g. estimation, testing and prediction.
In the first paper, the posterior distribution of the lag length in the vector autoregressive process is derived using the newly introduced fractional Bayes approach. Several properties of the posterior distribution are explored by analytical and simulation methods.
The second paper introduces a Bayesian reference analysis of the parameters in the cointegrated vector autoregression with a given number of long run relations. The novelty is the focus on the well-known fact that only the space spanned by the cointegration vectors, the cointegration space, is uniquely determined. The uniform distribution over the space of cointegration spaces is proposed as a reference prior for the cointegration vectors and the prior on the adjustment coefficients is chosen to make the overall prior consistent. A simple numerical evaluation of the posterior distribution based on Gibbs sampling is derived.
The third paper derives the posterior probability of restrictions on the cointegration space. Such posterior probabilities have several important advantages over traditional test of hypotheses, e. g. they have a clear interpretation and are internally consistent in the sense that the conclusions are not dependent on the particular sequence of tests chosen. In a small simulation study, the performance of the Bayesian method was nearly uniformly better than the likelihood ratio test and always superior to the two most widely used information criteria.
The fourth and last paper presents a procedure for calculating the complete predictive distribution for a sequence of future values of the process. The uncertainty in the choice of long run relations is appropriately handled via an easily specified prior distribution. The procedure is applied to a seven-variable macroeconomic system with the purpose of forecasting inflation.
Key words: Bayesian inference, Cointegration, Estimation, Lag
length, Prediction, Restrictions.