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The Score Of Conditionally Heteroskedastic Dynamic Regression Models With Student T Innovations, An Lm Test For Multivariate Normality

Author

Listed:
  • Gabriele Fiorentini

    (Universidad de Alicante)

  • Enrique Sentana

    (CEMFI)

  • Giorgio Calzolari

    (University of Florence)

Abstract

We provide numerically reliable analytical expressions for the score of conditionally heteroskedastic dynamic regression models when the conditional distribution is multivariate $t$. We also derive one-sided and 2-sided LM tests for multivariate normality versus multivariate $t$ based on the first two moments of the (squared) norm of the standardised innovations evaluated at the Gaussian quasi-ML estimators of the conditional mean and variance parameters. We reinterpret them as specification tests for multivariate excess kurtosis, and show that they have power against leptokurtic alternatives. Finally, we analyse UK stock returns, and confirm that their conditional distribution has fat tails.

Suggested Citation

  • Gabriele Fiorentini & Enrique Sentana & Giorgio Calzolari, 2000. "The Score Of Conditionally Heteroskedastic Dynamic Regression Models With Student T Innovations, An Lm Test For Multivariate Normality," Working Papers. Serie AD 2000-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    • Handle: RePEc:ivi:wpasad:2000-33
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    References listed on IDEAS

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    1. Jurgen A. Doornik & Henrik Hansen, 2008. "An Omnibus Test for Univariate and Multivariate Normality," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 927-939, December.
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    5. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
    6. H. D. Vinod & B. D. McCullough, 1999. "Corrigenda: The Numerical Reliability of Econometric Software," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1565-1565, December.
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    9. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
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    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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