Modelling multivariate skewness in financial returns: a SGARCH approach

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.