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Consistent Model Specification Tests Against Smooth Transition Alternatives

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  • 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.

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File URL: http://128.118.178.162/eps/em/papers/0402/0402004.pdf
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Bibliographic 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://128.118.178.162

Related research

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

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References

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  1. Corradi, V. & Swanson, N.R., 2000. "A Consistent Test for Nonlinear Out of Sample Predictive Accuracy," Discussion Papers 0012, Exeter University, Department of Economics.
  2. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
  3. repec:cup:macdyn:v:3:y:1999:i:3:p:311-40 is not listed on IDEAS
  4. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
  5. Alvaro Escribano & Oscar Jorda, . "Improved Testing And Specification Of Smooth Transition Regression Models," Department of Economics 97-26, California Davis - Department of Economics.
  6. 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.
  7. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, Econometric Society, vol. 53(5), pages 1047-70, September.
  8. Bierens, H.J. & Ploberger, W., 1995. "Asymptotic theory of integrated conditional moment tests," Discussion Paper, Tilburg University, Center for Economic Research 1995-124, Tilburg University, Center for Economic Research.
  9. 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.
  10. van Dijk, D.J.C. & Terasvirta, T. & Franses, Ph.H.B.F., 2000. "Smooth transition autoregressive models - A survey of recent developments," Econometric Institute Research Papers EI 2000-23/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  11. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  12. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  13. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, Econometric Society, vol. 64(2), pages 413-30, March.
  14. van Dijk, D.J.C. & Franses, Ph.H.B.F., 1997. "Modelling Multiple Regimes in the Business Cycle," Econometric Institute Research Papers EI 9734/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  15. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, Econometric Society, vol. 58(6), pages 1443-58, November.
  16. 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.
  17. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
  18. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
  19. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, Biometrika Trust, vol. 89(2), pages 484-489, June.
  20. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, Econometric Society, vol. 62(6), pages 1383-1414, November.
  21. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, Econometric Society, vol. 63(5), pages 1133-59, September.
  22. 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.
  23. 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.
  24. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, Econometric Society, vol. 50(3), pages 749-59, May.
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