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Bayes Estimators of the Cointegration Space

Author

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  • Villani, Mattias

    () (Research Department, Central Bank of Sweden)

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.

Suggested Citation

  • Villani, Mattias, 2003. "Bayes Estimators of the Cointegration Space," Working Paper Series 150, Sveriges Riksbank (Central Bank of Sweden).
  • Handle: RePEc:hhs:rbnkwp:0150
    as

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    File URL: http://www.riksbank.com/upload/8104/WP_150.pdf
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    References listed on IDEAS

    as
    1. 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 185-195, January.
    2. 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.
    3. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    4. 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.
    5. 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).
    6. Phillips, P C B, 1991. "Optimal Inference in Cointegrated Systems," Econometrica, Econometric Society, vol. 59(2), pages 283-306, March.
    7. 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.
    8. 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.
    9. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
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    More about this item

    Keywords

    Bayesian inference; Cointegration analysis; Estimation; Grassman manifold; Subspaces.;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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