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Modelling multivariate skewness in financial returns: a SGARCH approach

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  • Giovanni De Luca
  • Nicola Loperfido

Abstract

Skewness of financial time series is a relevant topic, due to its implications for portfolio theory and for statistical inference. In the univariate case, its default measure is the third cumulant of the standardized random variable. It can be generalized to the third multivariate cumulant that is a matrix containing all centered moments of order three which can be obtained from a random vector. The present paper examines some properties of the third cumulant under the assumptions of the multivariate SGARCH model introduced by De Luca, Genton, and Loperfido [2006. A multivariate skew-GARCH model. Advances in Econometrics 20: 33-57]. In the first place, it allows for parsimonious modelling of multivariate skewness. In the second place, all its elements are either null or negative, consistently with previous empirical and theoretical findings. A numerical example with financial returns of France, Spain and Netherlands illustrates the theoretical results in the paper.

Suggested Citation

  • Giovanni De Luca & Nicola Loperfido, 2015. "Modelling multivariate skewness in financial returns: a SGARCH approach," The European Journal of Finance, Taylor & Francis Journals, vol. 21(13-14), pages 1113-1131, November.
    • Handle: RePEc:taf:eurjfi:v:21:y:2015:i:13-14:p:1113-1131
    DOI: 10.1080/1351847X.2011.640342
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    Cited by:

    1. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
    2. Po Yun & Chen Zhang & Yaqi Wu & Xianzi Yang & Zulfiqar Ali Wagan, 2020. "A Novel Extended Higher-Order Moment Multi-Factor Framework for Forecasting the Carbon Price: Testing on the Multilayer Long Short-Term Memory Network," Sustainability, MDPI, vol. 12(5), pages 1-16, March.
    3. Taras Bodnar & Stepan Mazur & Nestor Parolya, 2019. "Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix‐variate location mixture of normal distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 636-660, June.
    4. Loperfido, Nicola, 2013. "Skewness and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 93-99.
    5. Loperfido, Nicola, 2014. "A note on the fourth cumulant of a finite mixture distribution," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 386-394.
    6. Loperfido, Nicola, 2014. "Linear transformations to symmetry," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 186-192.
    7. Mauro Bernardi & Leopoldo Catania, 2016. "Portfolio Optimisation Under Flexible Dynamic Dependence Modelling," Papers 1601.05199, arXiv.org.

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