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Consistent Model Specification Tests Against Smooth Transition Alternatives

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Author Info
Jonathan B. Hill (Florida International University)

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Abstract

In this paper we develop tests of functional form that are consistent against a class of nonlinear "smooth transition" models of the conditional mean. Our method is an extension of the consistent model specification tests developed by Bierens (1990), de Jong (1996) and Bierens and Ploberger (1997), provides maximal power against nonlinear smooth transition ARX specifications, and is consistent against any deviation from the null hypothesis. Of separate interest, we provide substantial detail regarding when and whether Bierens-type tests are asymptotically degenerate. In a simulation experiment in which all parameters are randomly selected, and a linear AR null model is selected by minimizing the AIC, the proposed test has power nearly identical to a most powerful test for true STAR processes, and dominates popular tests.

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File URL: http://129.3.20.41/eps/em/papers/0402/0402004.pdf
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Publisher Info
Paper provided by EconWPA in its series Econometrics with number 0402004.

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Length: 35 pages
Date of creation: 05 Feb 2004
Date of revision: 01 Mar 2004
Handle: RePEc:wpa:wuwpem:0402004

Note: Type of Document - pdf; prepared on WinXP; pages: 35
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Web page: http://129.3.20.41

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Related research
Keywords: smooth transition; consistent test; nondegenerate test; nonlinear; neural networks.;

Other versions of this item:

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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References listed on IDEAS
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  1. Corradi, Valentina & Swanson, Norman R., 2002. "A consistent test for nonlinear out of sample predictive accuracy," Journal of Econometrics, Elsevier, vol. 110(2), pages 353-381, October. [Downloadable!] (restricted)
    Other versions:
  2. Skalin, Joakim, 1998. "Testing linearity against smooth transition autoregression using a parametric bootstrap," Working Paper Series in Economics and Finance 276, Stockholm School of Economics, revised 13 Dec 1998. [Downloadable!]
  3. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November. [Downloadable!] (restricted)
    Other versions:
  4. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32. [Downloadable!] (restricted)
  5. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September. [Downloadable!] (restricted)
    Other versions:
  6. Dijk, Dick van & Franses, Philip Hans, 1999. "Modeling Multiple Regimes in the Business Cycle," Macroeconomic Dynamics, Cambridge University Press, vol. 3(03), pages 311-340, September. [Downloadable!]
  7. 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. [Downloadable!] (restricted)
    Other versions:
  8. repec:cup:macdyn:v:3:y:1999:i:3:p:311-40 is not listed on IDEAS
  9. Alvaro Escribano & Oscar Jorda, . "Improved Testing And Specification Of Smooth Transition Regression Models," Department of Economics 97-26, California Davis - Department of Economics. [Downloadable!]
  10. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April. [Downloadable!] (restricted)
  11. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  12. D. van Dijk & T. Terasvirta & P.H. Franses, 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Report 200, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
    Other versions:
  13. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November. [Downloadable!] (restricted)
    Other versions:
  14. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December. [Downloadable!] (restricted)
  15. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    Other versions:
  16. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May. [Downloadable!] (restricted)
  17. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December. [Downloadable!] (restricted)
  18. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September. [Downloadable!] (restricted)
  19. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(03), pages 295-325, June. [Downloadable!]
  20. Chung-Ming Kuan & Halbert White, 1992. "Artificial Neural Networks: An Econometric Perspective," University of California at San Diego, Economics Working Paper Series 92-11, Department of Economics, UC San Diego.
    Other versions:
  21. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January. [Downloadable!] (restricted)
  22. Van Dijk, D. & Franses, P.H., 1997. "Modelling Multiple Regimes in the Business Cycle," Papers 9734/a, Erasmus University of Rotterdam - Econometric Institute.
  23. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October. [Downloadable!] (restricted)
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