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LM-Tests for Linearity Against Smooth Transition Alternatives: A Bootstrap Simulation Study

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  • Jonathan B. Hill

    ()
    (Department of Economics, Florida International University)

Abstract

The universal method for testing linearity against smooth transition autoregressive (STAR) alternatives is the linearization of the STAR model around the null nuisance parameter value, and performing F-tests on polynomial regressions in the spirit of the RESET test. Polynomial regressors, however, are poor proxies for the nonlinearity associated with STAR processes, and are not consistent (asymptotic power of one) against STAR alternatives, let alone general deviations from the null. Moreover, the most popularly used STAR forms of nonlinearity, exponential and logistic, are known to be exploitable for consistent conditional moment tests of functional form, cf. Bierens and Ploberger (1997). In this paper, pushing asymptotic theory aside, we compare the small sample performance of the standard polynomial test with an essentially ignored consistent conditional moment test of linear autoregression against smooth transition alternatives. In particular, we compute an LM sup-statistic and characterize the asymptotic p-value by Hansen's (1996) bootstrap method. In our simulations, we randomly select all STAR parameters in order not to bias experimental results based on the use of "safe", "interior" parameter values that exaggerate the smooth transition nonlinearity. Contrary to past studies, we find that the traditional polynomial regression method performs only moderately well, and that the LM sup-test out-performs the traditional test method, in particular for small samples and for LSTAR processes.

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File URL: http://casgroup.fiu.edu/pages/docs/2245/1280267970_04-12.pdf
File Function: Revised version, 2004
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Bibliographic Info

Paper provided by Florida International University, Department of Economics in its series Working Papers with number 0412.

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Length: 13 pages
Date of creation: Jul 2004
Date of revision:
Handle: RePEc:fiu:wpaper:0412

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Keywords: Smooth transition AR; consistent conditional moment test; Lagrange Multiplier; bootstrap;

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  1. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(04), pages 435-451, December.
  2. 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.
  3. 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.
  4. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  5. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
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  7. 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.
  8. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-58, November.
  9. 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.
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  12. repec:cup:etheor:v:8:y:1992:i:4:p:435-51 is not listed on IDEAS
  13. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
  14. van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000. "Smooth Transition Autoregressive Models - A Survey of Recent Developments," Working Paper Series in Economics and Finance 380, Stockholm School of Economics, revised 17 Jan 2001.
  15. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-59, May.
  16. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  17. 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.
  18. 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.
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