On the least squares estimation of multiple-regime threshold autoregressive models
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.
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.
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.
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.:
- Coakley, Jerry & Fuertes, Ana-Marı́a & Pérez, Marı́a-Teresa, 2003.
"Numerical issues in threshold autoregressive modeling of time series,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 27(11), pages 2219-2242.
- Coakley, Jerry & Fuertes, Ana-Maria & Perez, Maria-Teresa, 2003. "Numerical issues in threshold autoregressive modeling of time series," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11-12), pages 2219-2242, September.
- 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.
- 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.
- 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.
- Jesús Gonzalo & Michael Wolf, 2001.
"Subsampling inference in threshold autoregressive models,"
Economics Working Papers
573, Department of Economics and Business, Universitat Pompeu Fabra.
- Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
- 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;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 335-369, December.
- Bruce E. Hansen & Mehmet Caner, 1997.
"Threshold Autoregressions with a Unit Root,"
Boston College Working Papers in Economics
381, Boston College Department of Economics.
- 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.
- Tom Doan, . "BAIPERRON: RATS procedure to perform Bai-Perron Test for Multiple Structural Changes," Statistical Software Components RTS00013, Boston College Department of Economics.
- Tom Doan, . "MULTIPLEBREAKS: RATS procedure to perform multiple structural change analysis," Statistical Software Components RTS00138, Boston College Department of Economics.
- Tom Doan, . "RATS programs to replicate examples of Bai-Perron procedure," Statistical Software Components RTZ00008, Boston College Department of Economics.
- BAI, Jushan & PERRON, Pierre, 1998. "Computation and Analysis of Multiple Structural-Change Models," Cahiers de recherche 9807, Universite de Montreal, Departement de sciences economiques.
- Hansen Bruce E., 1997.
"Inference in TAR Models,"
Studies in Nonlinear Dynamics & Econometrics,
De Gruyter, vol. 2(1), pages 1-16, April.
- Tom Doan, . "THRESHTEST: RATS procedure to perform Hansen's Test for Threshold Break," Statistical Software Components RTS00210, Boston College Department of Economics.
- 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.
- Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
- 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.
- 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.
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: (Shamier, Wendy)
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.