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.
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- 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.
- 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.
- 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.
- Mehmet Caner & Bruce E. Hansen, 2001.
"Threshold Autoregression with a Unit Root,"
Econometric Society, vol. 69(6), pages 1555-1596, November.
- 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, 2000.
"Sample Splitting and Threshold Estimation,"
Econometric Society, vol. 68(3), pages 575-604, May.
- 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.
- BAI, Jushan & PERRON, Pierre, 1998.
"Computation and Analysis of Multiple Structural-Change Models,"
Cahiers de recherche
9807, Universite de Montreal, Departement de sciences economiques.
- 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.
- 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.
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