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A new class of multivariate skew densities, with application to GARCH models

Luc Bauwens () and Sébastien Laurent ()

No 2002020, CORE Discussion Papers from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: 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.

Keywords: multivariate skew density; multivariate Student density; multivariate GARCH models (search for similar items in EconPapers)
JEL-codes: C13 C32 C52 (search for similar items in EconPapers)
Date: 2002-04
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Working Paper: A New Class of Multivariate skew Densities, with Application to GARCH Models (2002)
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