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A New Class of Multivariate skew Densities, with Application to GARCH Models


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  • Luc Bauwens
  • Sébastien Laurent


We propose a practical and flexible solution to introduce skewness in multivariate symmetrical distributions. Applying this procedure to the multivariate Student density leads to a "multivariate skew-Student" density, for which each marginal has a different asymmetry coefficient. Similarly, when applied to the product of independent univariate Student densities, it provides a "multivariate skew density with independent Student components" for which each marginal has a different asymmetry coefficient and number of degrees of freedom. Combined with a multivariate GARCH model, this new family of distributions (that generalizes the work of Fernandez and Steel, 1998) is potentially useful for modelling stock returns, which a are known to be conditionally heteroskedastic, fat-tailed, and often skew. In an application to the daily returns of the CAC40, NASDAQ, NIKKEI and the SMI, it is found that this density suits well the data and clearly outperforms its symmetric competitors.

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Bibliographic Info

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2002 with number 5.

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Date of creation: 01 Jul 2002
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Handle: RePEc:sce:scecf2:5

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Keywords: Multivariate skewness; Multivariate Student density; Multivariate GARCH models.;

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