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Estimating and Testing Threshold Regression Models with Multiple Threshold Variables

  • Chong, Terence Tai Leung
  • Yan, Isabel K.

Conventional threshold models contain only one threshold variable. This paper provides the theoretical foundation for threshold models with multiple threshold variables. The new model is very different from a model with a single threshold variable as several novel problems arisefrom having an additional threshold variable. First, the model is not analogous to a change-point model. Second, the asymptotic joint distribution of the threshold estimators is difficult to obtain. Third, the estimation time increases exponentially with the number of threshold variables. This paper derives the consistency and the asymptotic joint distribution of the threshold estimators. A fast estimation algorithm to estimate the threshold values is proposed. We also develop tests for the number of threshold variables. The theoretical results are supported by simulation experiments. Our model is applied to the study of currency crises.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 54732.

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Date of creation: 24 Mar 2014
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Handle: RePEc:pra:mprapa:54732
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  1. repec:oup:restud:v:68:y:2001:i:3:p:633-63 is not listed on IDEAS
  2. Flood, Robert P. & Garber, Peter M., 1984. "Collapsing exchange-rate regimes : Some linear examples," Journal of International Economics, Elsevier, vol. 17(1-2), pages 1-13, August.
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  9. Chong, Terence Tai-Leung, 2001. "Structural Change In Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 17(01), pages 87-155, February.
  10. Graciela L. Kaminsky, 1998. "Currency and banking crises: the early warnings of distress," International Finance Discussion Papers 629, Board of Governors of the Federal Reserve System (U.S.).
  11. Chang, R. & Velasco, A., 1998. "Financial Fragility and the Exchange Rate Regime," Working Papers 98-05, C.V. Starr Center for Applied Economics, New York University.
  12. Astatkie, T. & Watts, D. G. & Watt, W. E., 1997. "Nested threshold autoregressive (NeTAR) models," International Journal of Forecasting, Elsevier, vol. 13(1), pages 105-116, March.
  13. 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.
  14. Yan, Isabel K. & Kakkar, Vikas, 2011. "Real Exchange Rates and Productivity: Evidence From Asia," MPRA Paper 35218, University Library of Munich, Germany.
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  16. Henry, Olan T & Olekalns, Nilss & Summers, Peter M, 2001. "Exchange Rate Instability: A Threshold Autoregressive Approach," The Economic Record, The Economic Society of Australia, vol. 77(237), pages 160-66, June.
  17. Michael Kumhof & Shujing Li & Isabel Yan, . "Balance of Payments Crises Under Inflation Targeting," Working Papers 00020, Stanford University, Department of Economics.
  18. Chen, Haiqiang & Chong, Terence Tai Leung & Bai, Jushan, 2012. "Theory and Applications of TAR Model with Two Threshold Variables," MPRA Paper 54527, University Library of Munich, Germany.
  19. 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.
  20. Maurice Obstfeld, 1984. "Rational and Self-Fulfilling Balance-of-Payments Crises," NBER Working Papers 1486, National Bureau of Economic Research, Inc.
  21. repec:oup:qjecon:v:107:y:1992:i:2:p:407-37 is not listed on IDEAS
  22. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
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  24. 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.
  25. 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.
  26. Roley, V Vance & Wheatley, Simon M, 1996. "Shifts in the Interest-Rate Response to Money Announcements: What Can We Say about When They Occur?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 135-38, January.
  27. Krugman, Paul, 1979. "A Model of Balance-of-Payments Crises," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 11(3), pages 311-25, August.
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