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Consistent and Non-Degenerate Model Specification Tests Against Smooth Transition Alternatives

  • Jonathan B. Hill

    ()

    (Department of Economics, Florida International University)

In this paper we develop a test of functional form that is consistent against any deviation from the null specification, and directs power towards a class of nonlinear "smooth transition" functional forms. Of separate interest, we provide new details regarding when and whether consistent parametric tests of functional form are asymptotically degenerate. A test of linear autoregression against smooth transition alternatives is never degenerate. Moreover, a test of Exponential STAR has surprising power and non-degeneracy attributes entirely associated with the choice of threshold. In a simulation experiment in which all parameters are randomly selected the proposed test has power nearly identical to the most powerful tests for true STAR, neural network and SETAR processes, and dominates popular tests. We apply the test to monthly U.S. output, money supply, prices and interest rates.

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File URL: http://casgroup.fiu.edu/pages/docs/2245/1280267955_04-06.pdf
File Function: Revised version, 2006
Download Restriction: no

Paper provided by Florida International University, Department of Economics in its series Working Papers with number 0406.

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Length: 19 pages
Date of creation: Apr 2004
Date of revision:
Handle: RePEc:fiu:wpaper:0406
Contact details of provider: Postal: Miami, FL 33199
Phone: (305) 348-2316
Fax: (305) 348-1524
Web page: http://casgroup.fiu.edu/Economics/

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  1. 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.
  2. Bierens, Herman J., 1987. "Armax model specification testing, with an application to unemployment in the Netherlands," Journal of Econometrics, Elsevier, vol. 35(1), pages 161-190, May.
  3. Lundbergh, Stefan & Teräsvirta, Timo, 2003. "A time series model for an exchange rate in a target zone with applications," SSE/EFI Working Paper Series in Economics and Finance 533, Stockholm School of Economics.
  4. Donald W.K. Andrews & Werner Ploberger, 1992. "Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative," Cowles Foundation Discussion Papers 1015, Cowles Foundation for Research in Economics, Yale University.
  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. Lundbergh, Stefan & Terasvirta, Timo & van Dijk, Dick, 2003. "Time-Varying Smooth Transition Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 104-21, January.
  7. 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.
  8. Medeiros, Marcelo & Veiga, Alvaro, 2000. "Diagnostic Checking in a Flexible Nonlinear Time Series Model," SSE/EFI Working Paper Series in Economics and Finance 386, Stockholm School of Economics, revised 15 Jan 2001.
  9. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October.
  10. Wooldridge, Jeffrey M., 1992. "A Test for Functional Form Against Nonparametric Alternatives," Econometric Theory, Cambridge University Press, vol. 8(04), pages 452-475, December.
  11. Phillip Rothman & Dick van Dijk & Philip Hans Franses, 2000. "A Multivariate STAR Analysis of the Relationship Between Money and Output," Working Papers 0012, East Carolina University, Department of Economics.
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  13. 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.
  14. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
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  16. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
  17. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  18. Donald W.K. Andrews & Werner Ploberger, 1993. "Admissibility of the Likelihood Ratio Test When a Nuisance Parameter Is Present OnlyUnder the Alternative," Cowles Foundation Discussion Papers 1058, Cowles Foundation for Research in Economics, Yale University.
  19. 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.
  20. 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).
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  22. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
  23. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
  24. González-Rivera Gloria, 1998. "Smooth-Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(2), pages 1-20, July.
  25. Lin, Chien-Fu Jeff & Terasvirta, Timo, 1994. "Testing the constancy of regression parameters against continuous structural change," Journal of Econometrics, Elsevier, vol. 62(2), pages 211-228, June.
  26. Terasvirta, Timo & van Dijk, Dick & Medeiros, Marcelo C., 2005. "Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination," International Journal of Forecasting, Elsevier, vol. 21(4), pages 755-774.
  27. repec:cup:macdyn:v:3:y:1999:i:3:p:311-40 is not listed on IDEAS
  28. repec:cup:etheor:v:8:y:1992:i:4:p:452-75 is not listed on IDEAS
  29. King, Maxwell L & Shively, Thomas S, 1993. "Locally Optimal Testing When a Nuisance Parameter Is Present Only under the Alternative," The Review of Economics and Statistics, MIT Press, vol. 75(1), pages 1-7, February.
  30. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  31. Bierens, Herman J., 1984. "Model specification testing of time series regressions," Journal of Econometrics, Elsevier, vol. 26(3), pages 323-353, December.
  32. 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.
  33. Herman J. BIERENS, 1991. "Least Squares Estimation of Linear and Nonlinear ARMAX Models under Data Heterogeneity," Annales d'Economie et de Statistique, ENSAE, issue 20-21, pages 143-169.
  34. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
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