Advanced Search
MyIDEAS: Login to save this article or follow this journal

On the least squares estimation of multiple-regime threshold autoregressive models

Contents:

Author Info

  • Li, Dong
  • Ling, Shiqing

Abstract

This paper studies the least squares estimator (LSE) of the multiple-regime threshold autoregressive (TAR) model and establishes its asymptotic theory. It is shown that the LSE is strongly consistent. When the autoregressive function is discontinuous over each threshold, the estimated thresholds are n-consistent and asymptotically independent, each of which converges weakly to the smallest minimizer of a one-dimensional two-sided compound Poisson process. The remaining parameters are n-consistent and asymptotically normal. The theory of Chan (1993) is revisited and a numerical approach is proposed to simulate the limiting distribution of the estimated threshold via simulating a related compound Poisson process. Based on the numerical result, one can construct a confidence interval for the unknown threshold. This issue is not straightforward and has remained as an open problem since the publication of Chan (1993). This paper provides not only a solution to this long-standing open problem, but also provides methodological contributions to threshold models. Simulation studies are conducted to assess the performance of the LSE in finite samples. The results are illustrated with an application to the quarterly U.S. real GNP data over the period 1947–2009.

Download Info

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.sciencedirect.com/science/article/pii/S0304407611002685
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 167 (2012)
Issue (Month): 1 ()
Pages: 240-253

as in new window
Handle: RePEc:eee:econom:v:167:y:2012:i:1:p:240-253

Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Asymptotic distribution; Compound Poisson process; Least squares estimation; Multiple-regime TAR model;

Find related papers by JEL classification:

References

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. Maria-Teresa Perez & Ana-Maria Fuertes & Jerry Coakley, 2001. "Numerical Issues in Threshold Autoregressive Modelling of Time Series," Working Papers wp01-09, Warwick Business School, Finance Group.
  2. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  3. Jesús Gonzalo & Michael Wolf, 2001. "Subsampling inference in threshold autoregressive models," Economics Working Papers 573, Department of Economics and Business, Universitat Pompeu Fabra.
  4. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-74, May-June.
  5. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
  6. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
  7. Gary Koop & Simon M. Potter, 2004. "Dynamic asymmetries in US unemployment," ESE Discussion Papers 15, Edinburgh School of Economics, University of Edinburgh.
  8. Oliver Linton & Myunghwan Seo, 2005. "A smoothed least squares estimator for threshold regression models," LSE Research Online Documents on Economics 4434, London School of Economics and Political Science, LSE Library.
  9. Christian Genest & Bruno Rémillard, 2004. "Test of independence and randomness based on the empirical copula process," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 13(2), pages 335-369, December.
  10. Hansen Bruce E., 1997. "Inference in TAR Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 2(1), pages 1-16, April.
  11. BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
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 in new window

Cited by:
  1. Dong Li & Shiqing Ling & Jean-Michel Zakoian, 2013. "Asymptotic Inference in Multiple-Threshold Nonlinear Time Series Models," Working Papers 2013-51, Centre de Recherche en Economie et Statistique.
  2. Zhu, Ke & Li, Wai Keung & Yu, Philip L.H., 2014. "Buffered autoregressive models with conditional heteroscedasticity: An application to exchange rates," MPRA Paper 53874, University Library of Munich, Germany.
  3. repec:wyi:wpaper:002206 is not listed on IDEAS
  4. Haiqiang Chen, 2013. "Robust Estimation and Inference for Threshold Models with Integrated Regressors," SFB 649 Discussion Papers SFB649DP2013-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. repec:wyi:journl:002203 is not listed on IDEAS

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:167:y:2012:i:1:p:240-253. 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: (Zhang, Lei).

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.