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The Score of Condionally Heteroskedastic Dynamic Regression Models with Student T Innovations, and an LM Test for Multivariate Normality

Author

Listed:
  • Fiorentini, G.
  • Sentana, E.
  • Calzolari, G.

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 two-sided LM tests for multivariate normality versus multivariate t based on the first two moments of the 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 lepkurtic alternatives. Finally, we analyse UK stock returns, and confirm that their conditional distribution has fat tails.

Suggested Citation

  • Fiorentini, G. & Sentana, E. & Calzolari, G., 2000. "The Score of Condionally Heteroskedastic Dynamic Regression Models with Student T Innovations, and an LM Test for Multivariate Normality," Papers 0007, Centro de Estudios Monetarios Y Financieros-.
    • Handle: RePEc:fth:cemfdt:0007
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    JEL classification:

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

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