IDEAS home Printed from https://ideas.repec.org/p/lec/leecon/05-13.html
   My bibliography  Save this paper

Efficient Posterior Simulation for Cointegrated Models with Priors On the Cointegration Space

Author

Listed:
  • Gary Koop
  • Roberto León-González
  • Rodney W. Strachan

Abstract

A message coming out of the recent Bayesian literature on cointegration is that it is important to elicit a prior on the space spanned by the cointegrating vectors (as opposed to a particular identified choice for these vectors). In this note, we discuss a sensible way of eliciting such a prior. Furthermore, we develop a collapsed Gibbs sampling algorithm to carry out efficient posterior simulation in cointegration models. The computational advantages of our algorithm are most pronounced with our model, since the form of our prior precludes simple posterior simulation using conventional methods (e.g. a Gibbs sampler involves non-standard posterior conditionals). However, the theory we draw upon implies our algorithm will be more efficient even than the posterior simulation methods which are used with identified versions of cointegration models.

Suggested Citation

  • Gary Koop & Roberto León-González & Rodney W. Strachan, 2005. "Efficient Posterior Simulation for Cointegrated Models with Priors On the Cointegration Space," Discussion Papers in Economics 05/13, Division of Economics, School of Business, University of Leicester, revised Apr 2006.
  • Handle: RePEc:lec:leecon:05/13
    as

    Download full text from publisher

    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp05-13.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. Chikuse, Yasuko, 1990. "The matrix angular central Gaussian distribution," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 265-274, May.
    4. Larsson, Rolf & Villani, Mattias, 2001. "A distance measure between cointegration spaces," Economics Letters, Elsevier, vol. 70(1), pages 21-27, January.
    5. Strachan, R.W. & van Dijk, H.K., 2004. "Valuing structure, model uncertainty and model averaging in vector autoregressive processes," Econometric Institute Research Papers EI 2004-23, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    7. Dorfman, Jeffrey H., 1995. "A numerical bayesian test for cointegration of AR processes," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 289-324.
    8. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501, Decembrie.
    9. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    10. 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.
    11. 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.
    12. Geweke, John, 1996. "Bayesian reduced rank regression in econometrics," Journal of Econometrics, Elsevier, vol. 75(1), pages 121-146, November.
    13. Koop, Gary, 1994. "An objective Bayesian analysis of common stochastic trends in international stock prices and exchange rates," Journal of Empirical Finance, Elsevier, vol. 1(3-4), pages 343-364, July.
    14. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luca Benati & Thomas A. Lubik, 2021. "Searching for Hysteresis," Working Paper 21-03, Federal Reserve Bank of Richmond.
    2. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2011. "Bayesian inference in a time varying cointegration model," Journal of Econometrics, Elsevier, vol. 165(2), pages 210-220.
    3. Sylvia Kaufmann & Johann Scharler, 2013. "Bank-Lending Standards, Loan Growth and the Business Cycle in the Euro Area," Working Papers 2013-34, Faculty of Economics and Statistics, Universität Innsbruck.
    4. 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.
    5. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney, 2012. "Bayesian model averaging in the instrumental variable regression model," Journal of Econometrics, Elsevier, vol. 171(2), pages 237-250.
    6. Jacek Osiewalski & Justyna Wróblewska & Kamil Makieła, 2020. "Bayesian comparison of production function-based and time-series GDP models," Empirical Economics, Springer, vol. 58(3), pages 1355-1380, March.
    7. Jochmann Markus & Koop Gary, 2015. "Regime-switching cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(1), pages 35-48, February.
    8. Chan, Joshua C.C. & Eisenstat, Eric & Strachan, Rodney W., 2020. "Reducing the state space dimension in a large TVP-VAR," Journal of Econometrics, Elsevier, vol. 218(1), pages 105-118.
    9. Katsuhiro Sugita, 2017. "Time Series Analysis of the US Term Structure of Interest Rates Using a Bayesian Markov Switching Cointegration Model," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 9(3), pages 49-56, March.
    10. Justyna Wróblewska & Anna Pajor, 2019. "One-period joint forecasts of Polish inflation, unemployment and interest rate using Bayesian VEC-MSF models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 11(1), pages 23-45, March.
    11. 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.
    12. Murasawa Yasutomo, 2022. "Bayesian multivariate Beveridge–Nelson decomposition of I(1) and I(2) series with cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 26(3), pages 387-415, June.
    13. Tsay, Ruey S. & Ando, Tomohiro, 2012. "Bayesian panel data analysis for exploring the impact of subprime financial crisis on the US stock market," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3345-3365.
    14. Eric Eisenstat & Joshua C.C. Chan & Rodney W. Strachan, 2018. "Reducing Dimensions in a Large TVP-VAR," Working Paper Series 43, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    15. Anna Pajor & Justyna Wróblewska, 2022. "Forecasting performance of Bayesian VEC-MSF models for financial data in the presence of long-run relationships," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 12(3), pages 427-448, September.
    16. Justyna Wróblewska, 2015. "Common Trends and Common Cycles – Bayesian Approach," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 7(2), pages 91-110, June.
    17. Justyna Wróblewska, 2009. "Bayesian Model Selection in the Analysis of Cointegration," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 1(1), pages 57-69, March.
    18. Krzysztof Osiewalski & Jacek Osiewalski, 2013. "A Long-Run Relationship between Daily Prices on Two Markets: The Bayesian VAR(2)–MSF-SBEKK Model," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 5(1), pages 65-83, March.
    19. Justyna Wróblewska, 2012. "Bayesian Analysis of Weak Form Polynomial Reduced Rank Structures in VEC Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(4), pages 253-267, December.
    20. Dąbrowski, Marek A. & Wróblewska, Justyna, 2020. "Insulating property of the flexible exchange rate regime: A case of Central and Eastern European countries," International Economics, Elsevier, vol. 162(C), pages 34-49.
    21. Peter McAdam & Kostas Mouratidis & Theodore Panagiotidis & Georgios Papapanagiotou, 2023. "European Trade & Growth Imbalances: An Analysis using a Sign-Restriction Bayesian-GVAR with Stochastic Volatility," Working Paper series 23-12, Rimini Centre for Economic Analysis.
    22. Dąbrowski, Marek A. & Wróblewska, Justyna, 2015. "Exchange rate as a shock absorber or a shock propagator in Poland and Slovakia - an approach based on Bayesian SVAR models with common serial correlation," MPRA Paper 61441, University Library of Munich, Germany.
    23. Justyna Wróblewska, 2011. "Bayesian Analysis of Weak Form Reduced Rank Structure in VEC Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 3(3), pages 169-186, September.
    24. Dąbrowski, Marek A. & Wróblewska, Justyna, 2016. "Exchange rate as a shock absorber in Poland and Slovakia: Evidence from Bayesian SVAR models with common serial correlation," Economic Modelling, Elsevier, vol. 58(C), pages 249-262.
    25. Heather M Anderson & Farshid Vahid, 2010. "VARs, Cointegration and Common Cycle Restrictions," Monash Econometrics and Business Statistics Working Papers 14/10, Monash University, Department of Econometrics and Business Statistics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Villani, Mattias, 2005. "Bayesian Inference of General Linear Restrictions on the Cointegration Space," Working Paper Series 189, Sveriges Riksbank (Central Bank of Sweden).
    3. Gary Koop & Roberto Leon-Gonzalez & Rodney Strachan, 2008. "Bayesian inference in a cointegrating panel data model," Advances in Econometrics, in: Bayesian Econometrics, pages 433-469, Emerald Group Publishing Limited.
    4. Rodney Strachan & Herman K. van Dijk, "undated". "Bayesian Model Averaging in Vector Autoregressive Processes with an Investigation of Stability of the US Great Ratios and Risk of a Liquidity Trap in the USA, UK and Japan," MRG Discussion Paper Series 1407, School of Economics, University of Queensland, Australia.
    5. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2011. "Bayesian inference in a time varying cointegration model," Journal of Econometrics, Elsevier, vol. 165(2), pages 210-220.
    6. Villani, Mattias, 2006. "Bayesian point estimation of the cointegration space," Journal of Econometrics, Elsevier, vol. 134(2), pages 645-664, October.
    7. Andrea Silvestrini, 2010. "Testing fiscal sustainability in Poland: a Bayesian analysis of cointegration," Empirical Economics, Springer, vol. 39(1), pages 241-274, August.
    8. 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.
    9. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2019. "Priors for the Long Run," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 565-580, April.
    10. Markus Jochmann & Gary Koop & Roberto Leon‐Gonzalez & Rodney W. Strachan, 2013. "Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(1), pages 62-81, January.
    11. 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.
    12. Rodney W. Strachan & Herman K. van Dijk, 2014. "Divergent Priors and Well Behaved Bayes Factors," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 6(1), pages 1-31, March.
    13. Prüser, Jan, 2023. "Data-based priors for vector error correction models," International Journal of Forecasting, Elsevier, vol. 39(1), pages 209-227.
    14. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
    15. Gary Koop & Simon M. Potter & Rodney W. Strachan, 2008. "Re-Examining the Consumption-Wealth Relationship: The Role of Model Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(2-3), pages 341-367, March.
    16. Villani, Mattias, 2003. "Bayes Estimators of the Cointegration Space," Working Paper Series 150, Sveriges Riksbank (Central Bank of Sweden).
    17. Strachan, Rodney W. & Inder, Brett, 2004. "Bayesian analysis of the error correction model," Journal of Econometrics, Elsevier, vol. 123(2), pages 307-325, December.
    18. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
    19. Jochmann Markus & Koop Gary, 2015. "Regime-switching cointegration," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(1), pages 35-48, February.
    20. Bin Jiang & Anastasios Panagiotelis & George Athanasopoulos & Rob Hyndman & Farshid Vahid, 2016. "Bayesian Rank Selection in Multivariate Regression," Monash Econometrics and Business Statistics Working Papers 6/16, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:lec:leecon:05/13. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Abbie Sleath (email available below). General contact details of provider: https://edirc.repec.org/data/deleiuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.