IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Asymptotic Inference in Multiple-Threshold Nonlinear Time Series Models

  • Dong Li

    ()

    (Tsinghua University)

  • Shiqing Ling

    (Hong kong University of Science and Technology)

  • Jean-Michel Zakoian

    ()

    (CREST)

This paper investigates a class of multiple-threshold models, called Multiple Threshold Double AR (MTDAR) models. A sufficient condition is obtained for the existence and uniqueness of a strictly stationary and ergodic solution to the first-order MTDAR model. We study the Quasi-Maximum Likelihood Estimator (QMLE) of the MTDAR model. The estimated thresholds are shown to be n-consistent, asymptotically independent, and to converge weakly to the smallest minimizer of a two-sided compound Poisson process. The remaining parameters are ?n-consistent and asymptotically multivariate normal. In particular, these results apply to the multiple threshold ARCH model, with or without AR part, and to the multiple threshold AR models with ARCH errors. A score-based test is also presented to determine the number of thresholds in MTDAR models. The limiting distribution is shown to be distribution-free and is easy to implement in practice. Simulation studies are conducted to assess the performance of the QMLE and our score-based test in finite samples. The results are illustrated with an application to the quarterly U.S. real GNP data over the period 1947–2013

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.crest.fr/images/docTravail2013/2013-51.pdf
File Function: Crest working paper version
Download Restriction: no

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-51.

as
in new window

Length: 27
Date of creation: Dec 2013
Date of revision:
Handle: RePEc:crs:wpaper:2013-51
Contact details of provider: Postal: 15 Boulevard Gabriel Peri 92245 Malakoff Cedex
Phone: 01 41 17 60 81
Web page: http://www.crest.fr
More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Bruce E. Hansen, 1996. "Sample Splitting and Threshold Estimation," Boston College Working Papers in Economics 319., Boston College Department of Economics, revised 12 May 1998.
  2. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-25, April-Jun.
  3. Shiqing Ling, 2004. "Estimation and testing stationarity for double-autoregressive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 63-78.
  4. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
  5. Francq, Christian & Roy, Roch & Zakoian, Jean-Michel, 2005. "Diagnostic Checking in ARMA Models With Uncorrelated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 532-544, June.
  6. Mika Meitz & Pentti Saikkonen, 2008. "Parameter estimation in nonlinear AR-GARCH models," CREATES Research Papers 2008-30, School of Economics and Management, University of Aarhus.
  7. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199.
  8. Gary Koop & Simon M. Potter, 2004. "Dynamic asymmetries in US unemployment," ESE Discussion Papers 15, Edinburgh School of Economics, University of Edinburgh.
  9. Jesús Gonzalo & Michael Wolf, 2001. "Subsampling inference in threshold autoregressive models," Economics Working Papers 573, Department of Economics and Business, Universitat Pompeu Fabra.
  10. Li, Dong & Ling, Shiqing & Li, Wai Keung, 2013. "Asymptotic Theory On The Least Squares Estimation Of Threshold Moving-Average Models," Econometric Theory, Cambridge University Press, vol. 29(03), pages 482-516, June.
  11. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
  12. Li, W K & Ling, Shiqing & McAleer, Michael, 2002. " Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-69, July.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2013-51. 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: (Florian Sallaberry)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.