IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/42804.html
   My bibliography  Save this paper

Orbital Priors for Time-Series Models

Author

Listed:
  • Kociecki, Andrzej

Abstract

We propose the unified approach to construct the non–informative prior for time–series econometric models that are invariant under some group of transformations. We show that this invariance property characterizes some of the most popular models hence the applicability of the proposed framework is quite general. The suggested prior enjoys many desirable properties both from the Bayesian and non–Bayesian perspective. We provide detailed derivations of our prior in many standard time–series models including, AutoRegressions (AR), Vector AutoRegressions (VAR), Structural VAR and Error Correction Models (ECM).

Suggested Citation

  • Kociecki, Andrzej, 2012. "Orbital Priors for Time-Series Models," MPRA Paper 42804, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:42804
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/42804/1/MPRA_paper_42804.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Waggoner, Daniel F. & Zha, Tao, 2003. "Likelihood preserving normalization in multiple equation models," Journal of Econometrics, Elsevier, vol. 114(2), pages 329-347, June.
    2. Sims, Christopher A., 1988. "Bayesian skepticism on unit root econometrics," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 463-474.
    3. Uhlig, Harald, 1994. "On Jeffreys Prior when Using the Exact Likelihood Function," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 633-644, August.
    4. 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.
    5. Ni, Shawn & Sun, Dongchu, 2003. "Noninformative priors and frequentist risks of bayesian estimators of vector-autoregressive models," Journal of Econometrics, Elsevier, vol. 115(1), pages 159-197, July.
    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. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-968, November.
    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. Schotman, Peter C & van Dijk, Herman K, 1991. "On Bayesian Routes to Unit Roots," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 387-401, Oct.-Dec..
    10. James Zidek, 1969. "A representation of Bayes invariant procedures in terms of Haar measure," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 291-308, December.
    11. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-364, Oct.-Dec..
    12. G. Datta & J. Ghosh, 1995. "Noninformative priors for maximal invariant parameter in group models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 4(1), pages 95-114, June.
    13. 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.
    14. Shawn Ni & Dongchu Sun, 2005. "Bayesian Estimates for Vector Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 105-117, January.
    15. Gary Chamberlain & Marcelo J. Moreira, 2009. "Decision Theory Applied to a Linear Panel Data Model," Econometrica, Econometric Society, vol. 77(1), pages 107-133, January.
    16. Villani, Mattias, 2005. "Bayesian Reference Analysis Of Cointegration," Econometric Theory, Cambridge University Press, vol. 21(2), pages 326-357, April.
    17. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238.
    18. Gary Chamberlain, 2007. "Decision Theory Applied to an Instrumental Variables Model," Econometrica, Econometric Society, vol. 75(3), pages 609-652, May.
    19. Zivot, Eric, 1994. "A Bayesian Analysis Of The Unit Root Hypothesis Within An Unobserved Components Model," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 552-578, August.
    20. Chao, J. C. & Phillips, P. C. B., 1998. "Posterior distributions in limited information analysis of the simultaneous equations model using the Jeffreys prior," Journal of Econometrics, Elsevier, vol. 87(1), pages 49-86, August.
    21. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
    22. 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.
    23. Zha, Tao, 1999. "Block recursion and structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 90(2), pages 291-316, June.
    Full references (including those not matched with items on IDEAS)

    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. 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. Mattias Villani, 2009. "Steady-state priors for vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 630-650.
    3. Marriott, John & Newbold, Paul, 2000. "The strength of evidence for unit autoregressive roots and structural breaks: A Bayesian perspective," Journal of Econometrics, Elsevier, vol. 98(1), pages 1-25, September.
    4. Marcet, Albert & Jarociński, Marek, 2010. "Autoregressions in small samples, priors about observables and initial conditions," Working Paper Series 1263, European Central Bank.
    5. Prüser, Jan, 2023. "Data-based priors for vector error correction models," International Journal of Forecasting, Elsevier, vol. 39(1), pages 209-227.
    6. Warne, Anders, 2006. "Bayesian inference in cointegrated VAR models: with applications to the demand for euro area M3," Working Paper Series 692, European Central Bank.
    7. Marek Jarocinski & Albert Marcet, 2014. "Contrasting Bayesian and Frequentist Approaches to Autoregressions: the Role of the Initial Condition," Working Papers 776, Barcelona School of Economics.
    8. Charley Xia and William Griffiths, 2012. "Bayesian Unit Root Testing: The Effect Of Choice Of Prior On Test Outcomes," Department of Economics - Working Papers Series 1152, The University of Melbourne.
    9. 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.
    10. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
    11. Magris Martin & Iosifidis Alexandros, 2021. "Approximate Bayes factors for unit root testing," Papers 2102.10048, arXiv.org, revised Feb 2021.
    12. Warne, Anders & Villani, Mattias, 2003. "Monetary policy analysis in a small open economy using Bayesian cointegrated structural VARs," Working Paper Series 296, European Central Bank.
    13. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2014. "On the Rise of Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 14-085/III, Tinbergen Institute, revised 04 Sep 2014.
    14. Waggoner, Daniel F. & Zha, Tao, 2003. "A Gibbs sampler for structural vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 349-366, November.
    15. Andrea Carriero & George Kapetanios & Massimiliano Marcellino, 2011. "Forecasting large datasets with Bayesian reduced rank multivariate models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(5), pages 735-761, August.
    16. 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.
    17. Tomasz Woźniak, 2016. "Bayesian Vector Autoregressions," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 49(3), pages 365-380, September.
    18. Jarociński, Marek & Marcet, Albert, 2019. "Priors about observables in vector autoregressions," Journal of Econometrics, Elsevier, vol. 209(2), pages 238-255.
    19. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    20. Warne, Anders & Coenen, Günter & Christoffel, Kai, 2010. "Forecasting with DSGE models," Working Paper Series 1185, European Central Bank.

    More about this item

    Keywords

    Bayesian; Model invariance; Groups; Free group action; Orbit; Right Haar measure; Orbital decomposition; Maximal invariant; Cross section; Intersubjective prior; Vector AutoRegression (VAR); Structural VAR; Error Correction Model (ECM);
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - 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
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

    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:pra:mprapa:42804. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.