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Priors, Posterior Odds and Lagrange Multiplier Statistics in Bayesian Analyses of Cointegration

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Author Info
Kleibergen, F.R.
Paap, R. (Erasmus Econometric Institute)

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Abstract

Using the standard linear model as a base, a unified theory of Bayesian Analyses of Cointegration Models is constructed. This is achieved by defining (natural conjugate) priors in the linear model and using the implied priors for the cointegration model. Using these priors, posterior results for the cointegration model are obtained using a Metropolis-Hasting sampler. To compare the cointegration models mutually and with the vector autoregressive model under stationarity, we use two strategies. The first strategy uses the Bayesian interpretation of a Lagrange Multiplier statistic. The second strategy compares the models using prior and posterior odds ratios. The latter enables us to compute prior and posterior distributions over the cointegration rank and shows close resemblance with the posterior information criterium from Phillips and Ploberger (1996). To show the applicability of the derived theory, the constructed procedures are applied to data from Johansen and Juselius (1990) and a few simulated data sets.

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Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number EI 9668-/A Revision_Date: 2009-07-29.

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Date of creation: 01 Jan 1996
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Handle: RePEc:dgr:eureir:1765001398

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Related research
Keywords: Bayesian analyses; cointegration; Lagrange multiplier statistics;

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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.:
  1. Robert B. Litterman, 1985. "Forecasting with Bayesian vector autoregressions five years of experience," Working Papers 274, Federal Reserve Bank of Minneapolis. [Downloadable!]
    Other versions:
  2. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Blackwell Publishing, vol. 53(4), pages 473-95, August. [Downloadable!] (restricted)
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  3. Dorfman, Jeffrey H., 1995. "A numerical bayesian test for cointegration of AR processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 289-324. [Downloadable!] (restricted)
  4. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November. [Downloadable!] (restricted)
  5. 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. [Downloadable!]
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  6. 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.
  7. Kleibergen, Frank & Dijk, Herman K. van, 1996. "Bayesian simultaneous equations analysis using reduced rank structures," Econometric Institute Report 47, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
  9. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1986. "Forecasting and conditional projection using realistic prior distribution," Staff Report 93, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  10. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November. [Downloadable!] (restricted)
  11. repec:cup:etheor:v:10:y:1994:i:3-4:p:774-808 is not listed on IDEAS
  12. 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. [Downloadable!] (restricted)
  13. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July. [Downloadable!] (restricted)
  14. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
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  15. Peter C.B. Phillips, 1987. "Partially Identified Econometric Models," Cowles Foundation Discussion Papers 845R, Cowles Foundation, Yale University, revised Aug 1988. [Downloadable!]
  16. Kleibergen, F. & Hoek, H., 1995. "Bayesian analysis of ARMA models using noninformative priors," Discussion Paper 116, Tilburg University, Center for Economic Research. [Downloadable!]
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  17. Kleibergen, F.R. & Van Dijk, H.K., 1993. "On the Shape of the Likelyhood/Posterior in Cointegration Models," Papers 9315-a, Erasmus University of Rotterdam - Econometric Institute.
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  18. Kleibergen, Frank, 1996. "Equality restricted random variables: densities and sampling algorithms," Econometric Institute Report 36, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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  19. Kleibergen, F., 1996. "Reduced rank regression using generalized method of moments estimators," Discussion Paper 20, Tilburg University, Center for Economic Research. [Downloadable!]
  20. 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. [Downloadable!] (restricted)
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  21. 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. [Downloadable!] (restricted)
  22. Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January. [Downloadable!] (restricted)
  23. 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. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Kirstin Hubrich & Helmut Lütkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor and Francis Journals, vol. 20(3), pages 247-318. [Downloadable!] (restricted)
    Other versions:
  2. Kleibergen, Frank & Dijk, Herman K. van, 1996. "Bayesian simultaneous equations analysis using reduced rank structures," Econometric Institute Report 47, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
    Other versions:
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