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Simultaneous Testing of Mean and Variance Structures in Nonlinear Time Series Models

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Author Info

  • Song Xi Chen

    (Guanghua School of Management, Peking University)

  • Jiti Gao

    ()
    (School of Economics, University of Adelaide)

Abstract

This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the variance components of the goodness of fit. To reduce the dependence of the test on a single pair of smoothing bandwidths, we construct an adaptive test by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. The test procedure is based on a bootstrap calibration to the distribution of the empirical likelihood test statistic. We demonstrate that the empirical likelihood test is able to distinguish local alternatives which are different from the null hypothesis at an optimal rate.

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File URL: http://www.economics.adelaide.edu.au/research/papers/doc/wp2010-28.pdf
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Bibliographic Info

Paper provided by University of Adelaide, School of Economics in its series School of Economics Working Papers with number 2010-28.

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Length: 56 pages
Date of creation: Oct 2010
Date of revision:
Handle: RePEc:adl:wpaper:2010-28

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Related research

Keywords: Bootstrap; empirical likelihood; goodness{of{ t test; kernel estimation; least squares empirical likelihood; rate-optimal test;

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References

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  11. Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics, London School of Economics and Political Science, LSE Library 6638, London School of Economics and Political Science, LSE Library.
  12. Chen, Song Xi & Gao, Jiti & Tang, Chenghong, 2005. "A test for model specification of diffusion processes," MPRA Paper 11976, University Library of Munich, Germany, revised Feb 2007.
  13. Li, Q. & Wang, Suojin, 1998. "A simple consistent bootstrap test for a parametric regression function," Journal of Econometrics, Elsevier, Elsevier, vol. 87(1), pages 145-165, August.
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  15. Juan Carlos Escanciano, 2006. "Joint Diagnostic Tests for Conditional Mean and Variance Specifications," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 02/06, School of Economics and Business Administration, University of Navarra.
  16. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, Princeton University Press, edition 1, volume 1, number 8355.
  17. Chen, Song Xi & Gao, Jiti, 2007. "An adaptive empirical likelihood test for parametric time series regression models," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 950-972, December.
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  19. Chen, Song Xi & Härdle, Wolfgang & Kleinow, Torsten, 2000. "An empirical likelihood goodness-of-fit test for time series," SFB 373 Discussion Papers 2001,1, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  20. Li, Qi, 1999. "Consistent model specification tests for time series econometric models," Journal of Econometrics, Elsevier, Elsevier, vol. 92(1), pages 101-147, September.
  21. Li, Gang, 2003. "Nonparametric likelihood ratio goodness-of-fit tests for survival data," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 86(1), pages 166-182, July.
  22. Gao, Jiti & King, Maxwell, 2004. "Adaptive Testing In Continuous-Time Diffusion Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 20(05), pages 844-882, October.
  23. Song Xi Chen & Hengjian Cui, 2006. "On Bartlett correction of empirical likelihood in the presence of nuisance parameters," Biometrika, Biometrika Trust, Biometrika Trust, vol. 93(1), pages 215-220, March.
  24. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  25. Chen, Xiaohong & Fan, Yanqin, 1999. "Consistent hypothesis testing in semiparametric and nonparametric models for econometric time series," Journal of Econometrics, Elsevier, Elsevier, vol. 91(2), pages 373-401, August.
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  27. Chen, Song Xi & Cui, Hengjian, 2007. "On the second-order properties of empirical likelihood with moment restrictions," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 492-516, December.
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