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Model Selection Uncertainty and Detection of Threshold Effecs

  • Jean-Yves Pitarakis

    (University of Southampton)

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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File URL: http://128.118.178.162/eps/em/papers/0409/0409013.pdf
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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
Contact details of provider: Web page: http://128.118.178.162

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  1. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  2. Filippo Altissimo & Giovanni L. Violante, 2001. "The non-linear dynamics of output and unemployment in the U.S," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(4), pages 461-486.
  3. Hansen, Bruce E., 2005. "Challenges For Econometric Model Selection," Econometric Theory, Cambridge University Press, vol. 21(01), pages 60-68, February.
  4. Mehmet Caner & Bruce E. Hansen, 2001. "Threshold Autoregression with a Unit Root," Econometrica, Econometric Society, vol. 69(6), pages 1555-1596, November.
  5. 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.
  6. Minxian Yang, 2002. "Lag length and mean break in stationary VAR models," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 374-387, 06.
  7. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  8. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
  9. Hansen,B.E., 1999. "Testing for linearity," Working papers 7, Wisconsin Madison - Social Systems.
  10. Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(02), pages 163-185, June.
  11. Gary Koop & Simon M. Potter, 2004. "Dynamic asymmetries in US unemployment," ESE Discussion Papers 15, Edinburgh School of Economics, University of Edinburgh.
  12. 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.
  13. 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.
  14. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
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