Title: The generalized precision matrix: Dependency in non-Gaussian settings, theory and financial applications
Authors: Gabriele Torri - University of Bergamo (Italy) [presenting]
Sandra Paterlini - University of Trento (Italy)
Emanuele Taufer - University of Trento (Italy)
Rosella Giacometti - University of Bergamo (Italy)
Gyorgy Terdik - University of Debrecen (Hungary)
Abstract: Multivariate financial time series are characterized by highly non-Gaussian distributions, showing fat tails and high levels of tail correlation. Due to these stylized facts, tools such as partial correlation networks cannot properly be used to characterize the interconnectivity structure of random variables. Starting from local dependency measures, we propose a generalization of the precision matrix that describes the interconnectivity structure of multivariate random variables in a single point of the probability space, in a region, or under any conditioning. We use a Gram-Charlier expansion of the density to show how this matrix is related to the traditional precision matrix, we then discuss several parametric cases, focusing on distribution with fat tails, and we illustrate financial applications.