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Bayes Estimators of the Cointegration Space

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Author Info
Villani, Mattias () (Research Department, Central Bank of Sweden)

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Abstract

A neglected aspect of the otherwise fairly well developed Bayesian analysis of cointegration is the point estimation of the cointegration space. It is pointed out here that, due to the well known non-identification of the cointegration vectors, the parameter space is not an inner product space and conventional Bayes estimators therefore stand without their usual decision theoretic foundation. We present a Bayes estimator of the cointegration space which takes the curved geometry of the parameter space into account. Contrary to many of the Bayes estimators used in the literature, this estimator is invariant to the ordering of the time series. A dimension invariant overall measure of cointegration space uncertainty is also proposed. A small simulation study shows that the Bayes estimator compares favorably to the maximum likelihood estimator.

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Publisher Info
Paper provided by Sveriges Riksbank (Central Bank of Sweden) in its series Working Paper Series with number 150.

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Length: 16 pages
Date of creation: 01 Sep 2003
Date of revision:
Handle: RePEc:hhs:rbnkwp:0150

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Postal: Sveriges Riksbank, SE-103 37 Stockholm, Sweden
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Related research
Keywords: Bayesian inference; Cointegration analysis; Estimation; Grassman manifold; Subspaces.;

Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions

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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. Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(06), pages 701-743, December. [Downloadable!]
    Other versions:
  2. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November. [Downloadable!] (restricted)
  3. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March. [Downloadable!] (restricted)
    Other versions:
  4. Kleibergen, Frank & Paap, Richard, 2002. "Priors, posteriors and bayes factors for a Bayesian analysis of cointegration," Journal of Econometrics, Elsevier, vol. 111(2), pages 223-249, December. [Downloadable!] (restricted)
    Other versions:
  5. 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. [Downloadable!] (restricted)
  6. 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.
    Other versions:
  7. Strachan, Rodney W, 2003. "Valid Bayesian Estimation of the Cointegrating Error Correction Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 185-95, January.
    Other versions:
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