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Bayesian Prediction with a Cointegrated Vector Autoregression

Author

Listed:
  • Villani, Mattias

    (Department of Statistics, Stockholm University)

Abstract
A complete procedure for calculating the joint predictive distribution of future observations based on the cointegrated vector autoregression is presented. The large degree of uncertainty in the choise of the cointegration vectors is incorporated into the analysis through a prior distribution on the cointegration vectors which allows the forecaster to realistically express his beliefs. This prior leads to a form of model averaging where the predictions from the models based on the different cointegration vectors are weighted together in an optimal way. The ideas of Litterman (1980) are adapted for the prior on the short run dynamics with a resulting prior which only depends on a few hyperparameters and is therefore easily specified. A straight forward numerical evaluation of the predictive distribution based on Gibbs sampling is proposed. The prediction procedure is applied to a seven variable system with focus on forecasting the Swedish inflation.

Suggested Citation

  • Villani, Mattias, 1999. "Bayesian Prediction with a Cointegrated Vector Autoregression," Working Paper Series 97, Sveriges Riksbank (Central Bank of Sweden).
    • Handle: RePEc:hhs:rbnkwp:0097
    as

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    File URL: http://www.riksbank.com/upload/3531/WP_97.pdf
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    References listed on IDEAS

    as
    1. McNees, Stephen K, 1986. "Forecasting Accuracy of Alternative Techniques: A Comparison of U.S. Macroeconomic Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 5-15, January.
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    4. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    5. McNees, Stephen K, 1986. "Forecasting Accuracy of Alternative Techniques: A Comparison of U.S. Macroeconomic Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 1-23, January.
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    8. 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.
    9. Thompson, Patrick A & Miller, Robert B, 1986. "Sampling the Future: A Bayesian Approach to Forecasting from Univariate Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 427-436, October.
    10. Kadiyala, K Rao & Karlsson, Sune, 1997. "Numerical Methods for Estimation and Inference in Bayesian VAR-Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 99-132, March-Apr.
    11. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
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    13. Litterman, Robert, 1986. "Forecasting with Bayesian vector autoregressions -- Five years of experience : Robert B. Litterman, Journal of Business and Economic Statistics 4 (1986) 25-38," International Journal of Forecasting, Elsevier, vol. 2(4), pages 497-498.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Karlsson, Sune, 2013. "Forecasting with Bayesian Vector Autoregression," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 791-897, Elsevier.
    2. Per Jansson & Anders Vredin, 2003. "Forecast‐Based Monetary Policy: The Case of Sweden," International Finance, Wiley Blackwell, vol. 6(3), pages 349-380, November.
    3. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2018. "Bayesian Vector Autoregressions," The Warwick Economics Research Paper Series (TWERPS) 1159, University of Warwick, Department of Economics.
    4. repec:spo:wpmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS
    5. Villani, Mattias, 2005. "Bayesian Inference of General Linear Restrictions on the Cointegration Space," Working Paper Series 189, Sveriges Riksbank (Central Bank of Sweden).
    6. Bruggeman, Annick & Donati, Paola & Warne, Anders, 2003. "Is the demand for euro area M3 stable?," Working Paper Series 255, European Central Bank.
    7. Rodney W. Strachan & Herman K. Van Dijk, 2013. "Evidence On Features Of A Dsge Business Cycle Model From Bayesian Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(1), pages 385-402, February.
    8. Gary Koop & Rodney Strachan & Herman van Dijk & Mattias Villani, 2004. "Bayesian Approaches to Cointegration," Discussion Papers in Economics 04/27, Division of Economics, School of Business, University of Leicester.
    9. Jan G. De Gooijer & Rob J. Hyndman, 2005. "25 Years of IIF Time Series Forecasting: A Selective Review," Monash Econometrics and Business Statistics Working Papers 12/05, Monash University, Department of Econometrics and Business Statistics.
    10. Jansson, Per & Vredin, Anders, 2001. "Forecast-based Monetary Policy in Sweden 1992-1998: A View from Within," Working Paper Series 120, Sveriges Riksbank (Central Bank of Sweden).
    11. Christoffel, Kai & Coenen, Gunter & Warne, Anders, 2007. "Conditional versus unconditional forecasting with the New Area-Wide Model of the euro area," MPRA Paper 76759, University Library of Munich, Germany.
    12. Hauzenberger Niko & Huber Florian & Pfarrhofer Michael & Zörner Thomas O., 2021. "Stochastic model specification in Markov switching vector error correction models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(2), pages 1-17, April.
    13. Patricio Jaramillo, 2009. "Estimación de VAR Bayesianos para la Economía Chilena," Revista de Analisis Economico – Economic Analysis Review, Universidad Alberto Hurtado/School of Economics and Business, vol. 24(1), pages 101-126, Junio.
    14. repec:bla:intfin:v:6:y:2003:i:3:p:349-80 is not listed on IDEAS
    15. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    16. Niko Hauzenberger & Michael Pfarrhofer & Luca Rossini, 2020. "Sparse time-varying parameter VECMs with an application to modeling electricity prices," Papers 2011.04577, arXiv.org, revised Apr 2023.
    17. Lenard Lieb & Stephan Smeekes, 2017. "Inference for Impulse Responses under Model Uncertainty," Papers 1709.09583, arXiv.org, revised Oct 2019.
    18. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2010. "Forecasting with DSGE models," Working Paper Series 1185, European Central Bank.
    19. Prüser, Jan, 2023. "Data-based priors for vector error correction models," International Journal of Forecasting, Elsevier, vol. 39(1), pages 209-227.
    20. Huber, Florian & Zörner, Thomas O., 2019. "Threshold cointegration in international exchange rates:A Bayesian approach," International Journal of Forecasting, Elsevier, vol. 35(2), pages 458-473.
    21. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2013. "Predictive likelihood comparisons with DSGE and DSGE-VAR models," Working Paper Series 1536, European Central Bank.
    22. John Galbraith & Greg Tkacz, 2007. "How Far Can Forecasting Models Forecast? Forecast Content Horizons for Some Important Macroeconomic Variables," Staff Working Papers 07-1, Bank of Canada.
    23. repec:hal:spmain:info:hdl:2441/27od5pb99881folvtfs8s3k16l is not listed on IDEAS

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    More about this item

    Keywords

    Bayesian; Cointegration; Inflation forecasting; Model averaging; Predictive density;
    All these keywords.

    JEL classification:

    • E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General

    NEP fields

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