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Estimation and Testing of Dynamic Models with Generalized Hyperbolic Innovations

  • Mencía, Javier
  • Sentana, Enrique

We analyse the Generalised Hyperbolic distribution adequacy to model kurtosis and asymmetries in multivariate conditionally heteroskedastic dynamic regression models. We standardise this distribution, obtain analytical expressions for the log-likelihood score, and explain how to evaluate the information matrix. We also derive tests for the null hypotheses of multivariate normal and Student t innovations, and decompose them into skewness and kurtosis components, from which we obtain more powerful one-sided versions. Finally, we present an empirical application to five NASDAQ sectorial stock returns that indicates that their conditional distribution is asymmetric and leptokurtic, which can be successfully exploited for risk management purposes.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5177.

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Date of creation: Aug 2005
Date of revision:
Handle: RePEc:cpr:ceprdp:5177
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  12. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
  13. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-46, October.
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  21. Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2004. "On the validity of the Jarque-Bera normality test in conditionally heteroskedastic dynamic regression models," Economics Letters, Elsevier, vol. 83(3), pages 307-312, June.
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