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


  • BAUWENS, Luc
  • LAURENT, Sébastien


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.

Suggested Citation

  • BAUWENS, Luc & LAURENT, Sébastien, 2002. "A new class of multivariate skew densities, with application to GARCH models," LIDAM Discussion Papers CORE 2002020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:2002020

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    multivariate skew density; multivariate Student density; multivariate GARCH models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection


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