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Model selection uncertainty and detection of threshold effects

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  • Pitarakis, J.

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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Paper provided by Economics Division, School of Social Sciences, University of Southampton in its series Discussion Paper Series In Economics And Econometrics with number 0409.

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Date of creation: 01 Jan 2004
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Handle: RePEc:stn:sotoec:0409

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  1. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
  2. 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.
  3. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  4. 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.
  5. 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.
  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. 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. Bruce E. Hansen & Mehmet Caner, 1997. "Threshold Autoregressions with a Unit Root," Boston College Working Papers in Economics 381, Boston College Department of Economics.
  9. Simon M. Potter, 1993. "A Nonlinear Approach to U.S. GNP," UCLA Economics Working Papers 693, UCLA Department of Economics.
  10. Hansen, Bruce E, 1999. " Testing for Linearity," Journal of Economic Surveys, Wiley Blackwell, vol. 13(5), pages 551-76, December.
  11. 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.
  12. Hansen, Bruce E., 2005. "Challenges For Econometric Model Selection," Econometric Theory, Cambridge University Press, vol. 21(01), pages 60-68, February.
  13. Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(02), pages 163-185, June.
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Cited by:
  1. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.

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