Cointegration Analysis Based on a Uniform Prior over the Space of Cointegration Spaces

Mattias Villani

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.

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