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).
(This abstract was borrowed from another version of this item.)
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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).
- Boswijk, H Peter, 1996. "Testing Identifiability of Cointegrating Vectors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 153-60, April.
- 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.
- 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.
- 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.
- Geweke, John, 1996.
"Bayesian reduced rank regression in econometrics,"
Journal of Econometrics,
Elsevier, vol. 75(1), pages 121-146, November.
- Phillips, Peter C.B. & Ploberger, Werner, 1994.
"Posterior Odds Testing for a Unit Root with Data-Based Model Selection,"
Cambridge University Press, vol. 10(3-4), pages 774-808, August.
- 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.
- 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.
- 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.
- Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
- Phillips, P.C.B., 1989.
"Partially Identified Econometric Models,"
Cambridge University Press, vol. 5(02), pages 181-240, August.
- 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.
- Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
- 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.
- repec:dgr:uvatin:19980025 is not listed on IDEAS
- 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.
- Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
- repec:dgr:uvatin:20010073 is not listed on IDEAS
- 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.
- Dorfman, Jeffrey H., 1995. "A numerical bayesian test for cointegration of AR processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 289-324.
- Peter C.B. Phillips, 1988.
"Optimal Inference in Cointegrated Systems,"
Cowles Foundation Discussion Papers
866R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1989.
- 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.
- 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 & 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.
When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:111:y:2002:i:2:p:223-249. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.