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Model Selection Uncertainty and Detection of Threshold Effecs

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  • Jean-Yves Pitarakis

    (University of Southampton)

Abstract

Inferences about the presence or absence of threshold type nonlinearities in TAR models are conducted within models whose lag length has been estimated in a preliminary stage. Typically the null hypothesis of linearity is then tested against a threshold alternative on which the estimated lag length is imposed on each regime. In this paper we evaluate the properties of test statistics for detecting the presence of threshold effects in autoregressive models when this model uncertainty is taken into account. We show that this approach may lead to important distortions when the underlying model has truly threshold effects by establishing the limiting properties of the estimated lag length in the mispecified linear autoregressive fit and assessing the impact of this model uncertainty on the power of the tests. We subsequently propose a full model selection based approach designed to jointly detect the presence of threshold effects and optimally specify its dynamics and compare its performance with the traditional test based approach

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 0409013.

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Length: 25 pages
Date of creation: 26 Sep 2004
Date of revision:
Handle: RePEc:wpa:wuwpem:0409013

Note: Type of Document - pdf; pages: 25
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Web page: http://128.118.178.162

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Keywords: Model Selection; Threshold Models; SETAR;

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References

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  1. Minxian Yang, 2002. "Lag length and mean break in stationary VAR models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 374-387, 06.
  2. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
  3. Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(02), pages 163-185, June.
  4. Gary Koop & Simon M. Potter, 2004. "Dynamic asymmetries in US unemployment," ESE Discussion Papers 15, Edinburgh School of Economics, University of Edinburgh.
  5. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
  6. Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers 693, UCLA Department of Economics.
  7. Altissimo, Filippo & Violante, Giovanni L, 2000. "The Nonlinear Dynamics of Output and Unemployment in the US," CEPR Discussion Papers 2475, C.E.P.R. Discussion Papers.
  8. Gonzalo, Jesus & Pitarakis, Jean-Yves, 1998. "Specification via model selection in vector error correction models," Economics Letters, Elsevier, vol. 60(3), pages 321-328, September.
  9. Hansen, Bruce E, 1999. " Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-76, December.
  10. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-30, March.
  11. 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.
  12. Hansen, Bruce E., 2005. "Challenges For Econometric Model Selection," Econometric Theory, Cambridge University Press, vol. 21(01), pages 60-68, February.
  13. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
  14. 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.
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Cited by:
  1. Michael McAller & Marcelo C. Medeiros, 2007. "A multiple regime smooth transition heterogeneous autoregressive model for long memory and asymmetries," Textos para discussão 544, Department of Economics PUC-Rio (Brazil).
  2. Hung-pin Lai, 2013. "Estimation of the threshold stochastic frontier model in the presence of an endogenous sample split variable," Journal of Productivity Analysis, Springer, vol. 40(2), pages 227-237, October.

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