IDEAS home Printed from
   My bibliography  Save this paper

Determining the Number of Regimes in a Threshold Autoregressive Model Using Smooth Transition Autoregressions


  • Strikholm, Birgit

    () (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    () (Dept. of Economic Statistics, Stockholm School of Economics)


In this paper we propose a method for determining the number of regimes in threshold autoregressive models using smooth transition autoregression as a tool. As the smooth transition model is just an approximation to the threshold autoregressive one, no asymptotic properties are claimed for the proposed method. Tests available for testing the adequacy of a smooth transition autoregressive model are applied sequentially to determine the number of regimes. A simulation study is performed in order to find out the finite-sample properties of the procedure and to compare it with two other procedures available in the literature. We find that our method works reasonably well for both single and multiple threshold models.

Suggested Citation

  • Strikholm, Birgit & Teräsvirta, Timo, 2005. "Determining the Number of Regimes in a Threshold Autoregressive Model Using Smooth Transition Autoregressions," SSE/EFI Working Paper Series in Economics and Finance 578, Stockholm School of Economics, revised 11 Feb 2005.
  • Handle: RePEc:hhs:hastef:0578 Note: This is an early version of the paper published under a different title in Econometrics Journal 9, 472-491 (2006).

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. 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.
    2. Andrés González & Timo Teräsvirta & Dick van Dijk & Yukai Yang, 1910. "Panel Smooth Transition Regression Models," CREATES Research Papers 2017-36, Department of Economics and Business Economics, Aarhus University.
    3. Hansen, Bruce E., 1999. "Threshold effects in non-dynamic panels: Estimation, testing, and inference," Journal of Econometrics, Elsevier, vol. 93(2), pages 345-368, December.
    4. Hansen, Bruce E, 1999. " Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-576, December.
    5. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
    6. repec:cup:etheor:v:13:y:1997:i:3:p:315-52 is not listed on IDEAS
    7. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    8. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    9. Bai, Jushan, 1997. "Estimating Multiple Breaks One at a Time," Econometric Theory, Cambridge University Press, vol. 13(03), pages 315-352, June.
    10. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
    11. George Kapetanios, 2003. "Threshold models for trended time series," Empirical Economics, Springer, vol. 28(4), pages 687-707, November.
    12. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    13. 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.
    14. Kapetanios, G., 1999. "Threshold Models for Trended Time Series," Cambridge Working Papers in Economics 9905, Faculty of Economics, University of Cambridge.
    15. Medeiros, Marcelo & Veiga, Alvaro & Resende, Mauricio, 2000. "A Combinatorial Approach to Piecewise Linear Time Series Analysis," SSE/EFI Working Paper Series in Economics and Finance 393, Stockholm School of Economics.
    16. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    17. Stephen Goldfeld & Richard Quandt, 1973. "The Estimation of Structural Shifts by Switching Regressions," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 2, number 4, pages 475-485 National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Galvão, Ana Beatriz, 2013. "Changes in predictive ability with mixed frequency data," International Journal of Forecasting, Elsevier, vol. 29(3), pages 395-410.
    2. Birgit Strikholm & Timo Teräsvirta, 2006. "A sequential procedure for determining the number of regimes in a threshold autoregressive model," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 472-491, November.
    3. Mohammad Mirbagherijam, 2014. "Thresholds Effect of Money Growth on Inflation in Iran," International Journal of Academic Research in Business and Social Sciences, Human Resource Management Academic Research Society, International Journal of Academic Research in Business and Social Sciences, vol. 4(9), pages 319-329, September.
    4. Strikholm, Birgit, 2006. "Determining the number of breaks in a piecewise linear regression model," SSE/EFI Working Paper Series in Economics and Finance 648, Stockholm School of Economics.
    5. Emilio Zanetti Chini, 2013. "Generalizing smooth transition autoregressions," CREATES Research Papers 2013-32, Department of Economics and Business Economics, Aarhus University.
    6. Ana Beatriz Galvão & Michael Artis & Massimiliano Marcellino, 2007. "The transmission mechanism in a changing world," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(1), pages 39-61.
    7. Lazzarini, S. G. & Madalozzo, R. C & Artes, R. & Siqueira, J. O., 2004. "Measuring trust: An experiment in Brazil," Insper Working Papers wpe_42, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    8. Matteo Modena, 2008. "The Term Structure and the Expectations Hypothesis: a Threshold Model," Working Papers 2008_36, Business School - Economics, University of Glasgow.
    9. Chang, Ya-Kai & Chen, Yu-Lun & Chou, Robin K. & Gau, Yin-Feng, 2013. "The effectiveness of position limits: Evidence from the foreign exchange futures markets," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4501-4509.
    10. Terasvirta, Timo, 2006. "Forecasting economic variables with nonlinear models," Handbook of Economic Forecasting, Elsevier.
    11. Shahbaba Babak, 2009. "Discovering Hidden Structures Using Mixture Models: Application to Nonlinear Time Series Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-21, May.
    12. Bilgili, Faik, 2012. "Linear and nonlinear TAR panel unit root analyses for solid biomass energy supply of European countries," Renewable and Sustainable Energy Reviews, Elsevier, vol. 16(9), pages 6775-6781.
    13. Ana Beatriz C. Galvao, 2006. "Structural break threshold VARs for predicting US recessions using the spread," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(4), pages 463-487.

    More about this item


    Model specification; model selection criterion; nonlinear modelling; sequential testing; switching regression;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:hhs:hastef:0578. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Helena Lundin). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.