Cointegration occurs when the long-run multiplier matrix of a vector autoregressive model exhibits rank reduction. Using a singular value decomposition of the unrestricted long-run multiplier matrix, we construct a parameter that reflects the presence of rank reduction. Priors and posteriors of the parameters of the cointegration model follow from conditional priors and posteriors of the unrestricted long-run multiplier matrix given that the parameter that reflects rank reduction is equal to zero. This idea leads to a complete Bayesian framework for cointegration analysis. It includes prior specification, simulation schemes for obtaining posterior distributions and determination of the cointegration rank via Bayes factors. We apply the proposed Bayesian cointegration analysis to the Danish data of Johansen and Juselius (Oxford Bull. Econom. Stat. 52 (1990) 169).

Bayes factors, Bayesian analysis, cointegration, rank reduction, singular value decomposition
Time-Series Models; Dynamic Quantile Regressions (jel C32), Model Evaluation and Testing (jel C52),
Journal of Econometrics
Erasmus Research Institute of Management

Kleibergen, F.R, & Paap, R. (2002). Priors, Posteriors and Bayes factors for a Bayesian Analysis of Cointegration. In Journal of Econometrics (Vol. 111, pp. 223–249). doi:10.1016/S0304-4076(02)00105-7