IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v29y2002i5p771-789.html
   My bibliography  Save this article

Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach

Author

Listed:
  • Man-Suk Oh
  • Dong Wan Shin

Abstract

A Markov chain Monte Carlo (MCMC) approach, called a reversible jump MCMC, is employed in model selection and parameter estimation for possibly non-stationary and non-linear time series data. The non-linear structure is modelled by the asymmetric momentum threshold autoregressive process (MTAR) of Enders & Granger (1998) or by the asymmetric self-exciting threshold autoregressive process (SETAR) of Tong (1990). The non-stationary and non-linear feature is represented by the MTAR (or SETAR) model in which one ( „ 1 ) of the AR coefficients is greater than one, and the other ( „ 2 ) is smaller than one. The other non-stationary and linear, stationary and nonlinear, and stationary and linear features, represented respectively by ( „ 1 = „ 2 = 1 ), ( „ 1 p „ 2 < 1 ) and ( „ 1 = „ 2 < 1 ), are also considered as possible models. The reversible jump MCMC provides estimates of posterior probabilities for these four different models as well as estimates of the AR coefficients „ 1 and „ 2 . The proposed method is illustrated by analysing six series of US interest rates in terms of model selection, parameter estimation, and forecasting.

Suggested Citation

  • Man-Suk Oh & Dong Wan Shin, 2002. "Bayesian model selection and parameter estimation for possibly asymmetric and non-stationary time series using a reversible jump Markov chain Monte Carlo approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(5), pages 771-789.
    • Handle: RePEc:taf:japsta:v:29:y:2002:i:5:p:771-789
    DOI: 10.1080/02664760120098829
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760120098829
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760120098829?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Balke, Nathan S & Fomby, Thomas B, 1997. "Threshold Cointegration," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(3), pages 627-645, August.
    2. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 119-136, Suppl. De.
    3. Sichel, Daniel E, 1993. "Business Cycle Asymmetry: A Deeper Look," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 224-236, April.
    4. Granger, C W J & Lee, T H, 1989. "Investigation of Production, Sales and Inventory Relationships Using Multicointegration and Non-symmetric Error Correction Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages 145-159, Supplemen.
    5. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    6. Koop, Gary & Potter, Simon M, 1999. "Dynamic Asymmetries in U.S. Unemployment," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(3), pages 298-312, July.
    7. Enders, Walter & Granger, Clive W J, 1998. "Unit-Root Tests and Asymmetric Adjustment with an Example Using the Term Structure of Interest Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 304-311, July.
    8. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    9. 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.
    10. Shin, Dong Wan & Lee, Oesook, 2001. "Tests for Asymmetry in Possibly Nonstationary Time Series Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 233-244, April.
    11. Oh, Man-Suk, 1999. "Estimation of posterior density functions from a posterior sample," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 411-427, February.
    12. Lee, Oesook & Shin, Dong Wan, 2001. "A note on stationarity of the MTAR process on the boundary of the stationarity region," Economics Letters, Elsevier, vol. 73(3), pages 263-268, December.
    13. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November.
    14. Lee, Oesook & Shin, Dong Wan, 2000. "On geometric ergodicity of the MTAR process," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 229-237, July.
    15. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    16. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-328, April.
    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. Lee, Oesook & Shin, Dong Wan, 2001. "A note on stationarity of the MTAR process on the boundary of the stationarity region," Economics Letters, Elsevier, vol. 73(3), pages 263-268, December.
    2. Enders, Walter & Siklos, Pierre L, 2001. "Cointegration and Threshold Adjustment," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 166-176, April.
    3. Enders, Walter & Ludlow, Jorge, 1998. "Estimating Time-Varying ARMA Models Using Fourier Coefficients," ISU General Staff Papers 199810010700001307, Iowa State University, Department of Economics.
    4. Shin, Dong Wan & Lee, Oesook, 2007. "Asymmetry and nonstationarity for a seasonal time series model," Journal of Econometrics, Elsevier, vol. 136(1), pages 89-114, January.
    5. Lee, Oesook & Shin, Dong Wan, 2000. "On geometric ergodicity of the MTAR process," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 229-237, July.
    6. Byeongseon Seo, 2004. "Testing for Nonlinear Adjustment in Smooth Transition Vector Error Correction Models," Econometric Society 2004 Far Eastern Meetings 749, Econometric Society.
    7. George Kapetanios & Yongcheol Shin, 2006. "Unit root tests in three-regime SETAR models," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 252-278, July.
    8. Dueker, Michael J. & Sola, Martin & Spagnolo, Fabio, 2007. "Contemporaneous threshold autoregressive models: Estimation, testing and forecasting," Journal of Econometrics, Elsevier, vol. 141(2), pages 517-547, December.
    9. Wan Shin, Dong & Lee, Oesook, 2003. "An instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models," Journal of Econometrics, Elsevier, vol. 115(1), pages 29-52, July.
    10. Enders, Walter & Sandler, Todd, 1998. "Transnational Terrorism in the Post-Cold War Era," ISU General Staff Papers 199804010800001308, Iowa State University, Department of Economics.
    11. Liu, Yamei, 2000. "Overfitting and forecasting: linear versus non-linear time series models," ISU General Staff Papers 2000010108000014914, Iowa State University, Department of Economics.
    12. Park, Soo Jung & Wan Shin, Dong & Uk Park, Byeong & Chul Kim, Woo & Oh, Man-Suk, 2005. "Bayesian test for asymmetry and nonstationarity in MTAR model with possibly incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1192-1204, June.
    13. Wang, Chong, 1998. "Testing for purchasing power parity: a nonlinear approach," ISU General Staff Papers 1998010108000013534, Iowa State University, Department of Economics.
    14. Kurmaş Akdoğan, 2017. "Unemployment hysteresis and structural change in Europe," Empirical Economics, Springer, vol. 53(4), pages 1415-1440, December.
    15. Andy Snell & George Kapetanios & Yongcheol Shin, 2004. "Testing for nonlinear cointegration between stock prices and dividends," Money Macro and Finance (MMF) Research Group Conference 2003 90, Money Macro and Finance Research Group.
    16. Nunes, Mauricio & Da Silva, Sergio, 2007. "Rational bubbles in emerging stockmarkets," MPRA Paper 4641, University Library of Munich, Germany.
    17. David G. McMillan, 2009. "Non-linear interest rate dynamics and forecasting: evidence for US and Australian interest rates," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 14(2), pages 139-155.
    18. Gonzalo, Jesùs & Pitarakis, Jean-Yves, 2005. "Threshold effects In multivariate error correction models," Discussion Paper Series In Economics And Econometrics 0501, Economics Division, School of Social Sciences, University of Southampton.
    19. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    20. Dilem Yildirim & Ralf Becker & Denise R Osborn, 2009. "Bootstrap Unit Root Tests for Nonlinear Threshold Models," Economics Discussion Paper Series 0915, Economics, The University of Manchester.

    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:taf:japsta:v:29:y:2002:i:5:p:771-789. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.