A New Class of Multivariate skew Densities, with Application to GARCH Models
AbstractWe 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 InfoPaper provided by Society for Computational Economics in its series Computing in Economics and Finance 2002 with number 5.
Date of creation: 01 Jul 2002
Date of revision:
Multivariate skewness; Multivariate Student density; Multivariate GARCH models.;
Other versions of this item:
- BAUWENS, Luc & LAURENT, Sébastien, 2002. "A new class of multivariate skew densities, with application to GARCH models," CORE Discussion Papers 2002020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
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