IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/81684a10-935f-49c4-b5ab-0ac35f7bfd2b.html
   My bibliography  Save this paper

Bayesian analysis of ARMA models using noninformative priors

Author

Listed:
  • Kleibergen, F.R.
  • Hoek, H.

Abstract

Parameters in AutoRegressive Moving Average (ARMA) models are locally nonidentified, due to the problem of root cancellation. Parameters can be constructed which represent this identification problem. We argue that ARMA parameters should be analyzed conditional on these identifying parameters. Priors exploiting this feature result in regular posteriors, while priors which neglect it result in posteriori favor of nonidentified parameter values. By considering the implicit AR representation of an ARMA model a prior with the desired proporties is obtained. The implicit AR representation also allows to construct easily implemented algorithms to analyze ARMA parameters. As a byproduct, posteriors odds ratios can be computed to compare (nonnested) parsimonious ARMA models. The procedures are applied to two datasets, the (extended) Nelson-Plosser data and monthly observations of US 3-month and 10 year interest rates. For approximately 50% of the series in these two datasets an ARMA model is favored above an AR model.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Kleibergen, F.R. & Hoek, H., 1995. "Bayesian analysis of ARMA models using noninformative priors," Other publications TiSEM 81684a10-935f-49c4-b5ab-0, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:81684a10-935f-49c4-b5ab-0ac35f7bfd2b
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/522675/116.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    2. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
    3. 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.
    4. DeJong, David N & Whiteman, Charles H, 1993. "Estimating Moving Average Parameters: Classical Pileups and Bayesian Posteriors," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(3), pages 311-317, July.
    5. 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..
    6. Sargan, J D & Bhargava, Alok, 1983. "Maximum Likelihood Estimation of Regression Models with First Order Moving Average Errors When the Root Lies on the Unit Circle," Econometrica, Econometric Society, vol. 51(3), pages 799-820, May.
    7. Schotman, Peter C., 1994. "Priors For The Ar(1) Model: Parameterization Issues and Time Series Considerations," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 579-595, August.
    8. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    9. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    10. 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.
    11. 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.
    12. Monahan, John F., 1983. "Fully Bayesian analysis of ARMA time series models," Journal of Econometrics, Elsevier, vol. 21(3), pages 307-331, April.
    13. Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January.
    14. 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..
    15. Kleibergen, Frank & van Dijk, Herman K., 1994. "Direct cointegration testing in error correction models," Journal of Econometrics, Elsevier, vol. 63(1), pages 61-103, July.
    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. Kleibergen, F.R. & Paap, R., 1996. "Priors, Posterior Odds and Lagrange Multiplier Statistics in Bayesian Analyses of Cointegration," Econometric Institute Research Papers EI 9668-/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.

    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. 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.
    2. Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
    3. 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.
    4. Nalan Basturk & Cem Cakmakli & S. Pinar Ceyhan & Herman K. van Dijk, 2013. "Historical Developments in Bayesian Econometrics after Cowles Foundation Monographs 10, 14," Tinbergen Institute Discussion Papers 13-191/III, Tinbergen Institute.
    5. Koop, Gary & Dijk, Herman K. Van, 2000. "Testing for integration using evolving trend and seasonals models: A Bayesian approach," Journal of Econometrics, Elsevier, vol. 97(2), pages 261-291, August.
    6. 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.
    7. Marcet, Albert & Jarociński, Marek, 2010. "Autoregressions in small samples, priors about observables and initial conditions," Working Paper Series 1263, European Central Bank.
    8. Kociecki, Andrzej, 2012. "Orbital Priors for Time-Series Models," MPRA Paper 42804, University Library of Munich, Germany.
    9. Gordon, Stephen & Bélanger, Gilles, 1996. "Échantillonnage de Gibbs et autres applications économétriques des chaînes markoviennes," L'Actualité Economique, Société Canadienne de Science Economique, vol. 72(1), pages 27-49, mars.
    10. Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(6), pages 701-743, December.
    11. de Pooter, M.D. & Ravazzolo, F. & Segers, R. & van Dijk, H.K., 2008. "Bayesian near-boundary analysis in basic macroeconomic time series models," Econometric Institute Research Papers EI 2008-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Steel, M.F.J., 1991. "Bayesian inference in time series," Discussion Paper 1991-53, Tilburg University, Center for Economic Research.
    13. Kim, Chang-Jin & Kim, Jaeho, 2013. "The `Pile-up Problem' in Trend-Cycle Decomposition of Real GDP: Classical and Bayesian Perspectives," MPRA Paper 51118, University Library of Munich, Germany.
    14. Chao, John C. & Phillips, Peter C. B., 2002. "Jeffreys prior analysis of the simultaneous equations model in the case with n+1 endogenous variables," Journal of Econometrics, Elsevier, vol. 111(2), pages 251-283, December.
    15. 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.
    16. van Dijk, H.K., 2002. "On Bayesian structural inference in a simultaneous equation model," Econometric Institute Research Papers EI 2002-10, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    17. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    18. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
    19. Gael M. Martin & David T. Frazier & Christian P. Robert, 2020. "Computing Bayes: Bayesian Computation from 1763 to the 21st Century," Monash Econometrics and Business Statistics Working Papers 14/20, Monash University, Department of Econometrics and Business Statistics.
    20. Lennart F. Hoogerheide & Johan F. Kaashoek, 2004. "Functional Approximations to Likelihoods/Posterior Densities: A Neural Network Approach to Efficient Sampling," Computing in Economics and Finance 2004 74, Society for Computational Economics.

    More about this item

    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:tiu:tiutis:81684a10-935f-49c4-b5ab-0ac35f7bfd2b. 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: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    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.