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Consistent Model Specification Tests Against Smooth Transition Alternatives

Author

Listed:
  • Jonathan B. Hill

    (Florida International University)

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.

Suggested Citation

  • Jonathan B. Hill, 2004. "Consistent Model Specification Tests Against Smooth Transition Alternatives," Econometrics 0402004, EconWPA, revised 05 Aug 2005.
  • Handle: RePEc:wpa:wuwpem:0402004
    Note: Type of Document - pdf; prepared on WinXP; pages: 35
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    File URL: http://econwpa.repec.org/eps/em/papers/0402/0402004.pdf
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    References listed on IDEAS

    as
    1. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
    2. Dick van Dijk & Timo Terasvirta & Philip Hans Franses, 2002. "Smooth Transition Autoregressive Models — A Survey Of Recent Developments," Econometric Reviews, Taylor & Francis Journals, vol. 21(1), pages 1-47.
    3. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    4. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    5. 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.
    6. 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.
    7. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    8. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, March.
    9. 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.
    10. Alvaro Escribano & Oscar Jorda, "undated". "Improved Testing And Specification Of Smooth Transition Regression Models," Department of Economics 97-26, California Davis - Department of Economics.
    11. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-1159, September.
    12. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
    13. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    14. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    15. 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.
    16. Skalin, Joakim, 1998. "Testing linearity against smooth transition autoregression using a parametric bootstrap," SSE/EFI Working Paper Series in Economics and Finance 276, Stockholm School of Economics, revised 13 Dec 1998.
    17. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    18. 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.
    19. 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.
    20. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-759, May.
    21. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
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    25. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
    26. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
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    More about this item

    Keywords

    smooth transition; consistent test; nondegenerate test; nonlinear; neural networks.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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, Validation, and Selection

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