Priors,posteriors and bayes factors for a Bayesian analysis of cointegration |
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| Institution: | 1. Department of Quantitative Economics, University of Amsterdam, NL-1018 WB Amsterdam, The Netherlands;2. Econometric Institute, Erasmus University, 3000 DR Rotterdam, The Netherlands;1. School of Automation, Guangdong Polytechnic Normal University, Guangzhou, China;2. Department of Computer Science and Information Engineering, College of Electrical and Computer Engineering, National Formosa University, Yunlin, Taiwan;3. Department of Industrial Engineering and Engineering Management, College of Engineering, National Tsing Hua University, Taiwan;4. Centre for Quantum Computation and Intelligent Systems, Advanced Analytics Institute, University of Technology, Sydney, Ultimo, Australia;1. Tobacco Policy Research Program, University of Kentucky College of Nursing, Lexington, Kentucky;2. Division of General Internal Medicine, and Center for Tobacco Control Research and Education, University of California San Francisco, San Francisco California |
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| Abstract: | 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). |
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