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First order asymptotic theory for parametric misspecification tests of GARCH models

  • Andreea Halunga
  • Chris D. Orme

This paper develops a framework for the construction and analysis of parametric misspecification tests for generalized autoregressive conditional heteroskedastic (GARCH) models, based on first-order asymptotic theory. The principal finding is that estimation effects from the correct specification of the conditional mean (regression) function can be asymptotically nonnegligible. This implies that certain procedures, such as the asymmetry tests of Engle and Ng (1993, Journal of Finance 48, 1749–1777) and the nonlinearity test of Lundbergh and Teräsvirta (2002, Journal of Econometrics 110, 417–435), are asymptotically invalid. A second contribution is the proposed use of alternative tests for asymmetry and/or nonlinearity that, it is conjectured, should enjoy improved power properties. A Monte Carlo study supports the principal theoretical findings and also suggests that the new tests have fairly good size and very good power properties when compared with the Engle and Ng (1993) and Lundbergh and Teräsvirta (2002) procedures.

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File URL: http://www.socialsciences.manchester.ac.uk/medialibrary/economics/discussionpapers/EDP-0721.pdf
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Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 0721.

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Date of creation: 2007
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Handle: RePEc:man:sespap:0721
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Web page: http://www.socialsciences.manchester.ac.uk/subjects/economics/

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  1. 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.
  2. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-21, May.
  3. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-35, April.
  4. Godfrey, Leslie G & Orme, Chris D, 1996. "On the Behavior of Conditional Moment Tests in the Presence of Unconsidered Local Alternatives," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 263-81, May.
  5. Felix Chan & Michael McAleer, 2003. "On the Structure, Asymptotic Theory and Applications of STAR-GARCH Models," CIRJE F-Series CIRJE-F-216, CIRJE, Faculty of Economics, University of Tokyo.
  6. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  7. Bai, Jushan & Ng, Serena, 2001. "A consistent test for conditional symmetry in time series models," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 225-258, July.
  8. Godfrey, Leslie G., 1996. "Some results on the Glejser and Koenker tests for heteroskedasticity," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 275-299.
  9. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  10. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  11. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  12. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  13. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  14. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  15. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
  16. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October.
  17. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
  18. Felix Chan & Michael McAleer, 2002. "Maximum likelihood estimation of STAR and STAR-GARCH models: theory and Monte Carlo evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 509-534.
  19. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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