Priors, posteriors and bayes factors for a Bayesian analysis of cointegration
Cointegration occurs when the long run multiplier of a vector autoregressive model exhibits rank reduction. Priors and posteriors of the parameters of the cointegration model are therefore proportional to priors and posteriors of the long run multiplier given that it has reduced rank. Rank reduction of the long run multiplier is modelled using a decomposition resulting from its singular value decomposition. It specifies the long run multiplier matrix as the sum of a matrix that equals the product of the adjustment parameters and the cointegrating vectors, i.e. the cointegration specification, and a matrix that models the deviation from cointegration. Priors and posteriors for the parameters of the cointegration model are obtained by restricting the latter matrix to zero in the prior and posterior of the unrestricted long run multiplier. The special decomposition of the long run multiplier results in unique posterior densities. This theory 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 illustrate the analysis with several simulated series, the UK data of Hendry and Doornik (1994) and the Danish data of Johansen and Juselius (1990).
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- Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
- Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
- John F. Geweke, 1995.
"Bayesian reduced rank regression in econometrics,"
540, Federal Reserve Bank of Minneapolis.
- Chao, John C. & Phillips, Peter C. B., 1999.
"Model selection in partially nonstationary vector autoregressive processes with reduced rank structure,"
Journal of Econometrics,
Elsevier, vol. 91(2), pages 227-271, August.
- John C. Chao & Peter C.B. Phillips, 1997. "Model Selection in Partially Nonstationary Vector Autoregressive Processes with Reduced Rank Structure," Cowles Foundation Discussion Papers 1155, Cowles Foundation for Research in Economics, Yale University.
- repec:dgr:uvatin:19980025 is not listed on IDEAS
- BAUWENS, Luc & LUBRANO , Michel, 1994.
"Identification Restrictions and Posterior Densities in Cointegrated Gaussian VAR Systems,"
CORE Discussion Papers
1994018, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bauwens, L. & Lubrano, M., . "Identification restrictions and posterior densities in cointegrated Gaussian VAR system," CORE Discussion Papers RP -1206, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Phillips, P C B, 1991.
"Optimal Inference in Cointegrated Systems,"
Econometric Society, vol. 59(2), pages 283-306, March.
- Phillips, P.C.B., 1989.
"Partially Identified Econometric Models,"
Cambridge University Press, vol. 5(02), pages 181-240, August.
- repec:dgr:uvatin:20010073 is not listed on IDEAS
- Koop, Gary, 1991. "Cointegration tests in present value relationships : A Bayesian look at the bivariate properties of stock prices and dividends," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 105-139.
- Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
- Peter C.B. Phillips & Werner Ploberger, 1992.
"Posterior Odds Testing for a Unit Root with Data-Based Model Selection,"
Cowles Foundation Discussion Papers
1017, Cowles Foundation for Research in Economics, Yale University.
- Phillips, Peter C.B. & Ploberger, Werner, 1994. "Posterior Odds Testing for a Unit Root with Data-Based Model Selection," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 774-808, August.
- Kleibergen, Frank & van Dijk, Herman K., 1998.
"Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures,"
Cambridge University Press, vol. 14(06), pages 701-743, December.
- Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers EI 9714/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-60, April.
- Johansen, Soren & Juselius, Katarina, 1990. "Maximum Likelihood Estimation and Inference on Cointegration--With Applications to the Demand for Money," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 52(2), pages 169-210, May.
- Kleibergen, Frank & van Dijk, Herman K., 1994. "Direct cointegration testing in error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 61-103, July.
- DeJong, David N., 1992. "Co-integration and trend-stationarity in macroeconomic time series : Evidence from the likelihood function," Journal of Econometrics, Elsevier, vol. 52(3), pages 347-370, June.
- Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August.
- Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
- Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-80, November.
- Shoesmith, Gary L., 1995. "Multiple cointegrating vectors, error correction, and forecasting with Litterman's model," International Journal of Forecasting, Elsevier, vol. 11(4), pages 557-567, December.
- Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, March.
- Dorfman, Jeffrey H., 1995. "A numerical bayesian test for cointegration of AR processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 289-324.
- Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
- Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
- Hendry, David F & Doornik, Jurgen A, 1994. "Modelling Linear Dynamic Econometric Systems," Scottish Journal of Political Economy, Scottish Economic Society, vol. 41(1), pages 1-33, February.
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