Mattias Villani
Abstract
A Bayesian inference on the parameters of the cointegrated vector autoregression
with a given number of long run relations is introduced. A new vague reference
prior is derived based 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 natural reference prior. The prior distribution on the adjustment
coefficients is chosen to make the overall prior consistent with respect
to the matrix of long run multipliers. The posterior distribution is obtained
by an easily implemented Gibbs sampler and the necessary full conditional
posteriors are derived. Posterior location and variation measures of the
cointegration space are introduced. The procedure is illustrated on US
consumption-income data. A small simulation study compares the (frequency)
performance of the Bayes procedure to the maximum likelihood estimator.
Keywords: Bayesian Inference, Cointegration, Reference prior, Posterior
location and variation measures.