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Title: Dependency in non-Gaussian settings: The generalized precision matrix and its financial applications Authors:  Gabriele Torri - VSB TU Ostrava (Czech Republic) [presenting]
Sandra Paterlini - University of Trento (Italy)
Emanuele Taufer - University of Trento (Italy)
Rosella Giacometti - VSB-TU Ostrava,Czech Republic (Czech Republic)
Abstract: Partial correlation networks allow studying the interconnectivity of a financial system. Still, outside the Gaussian framework, they do not allow to fully characterize the interconnectivity structure of random variables. This severely limits its applications in finance where distributions with fat tails and high levels of tail correlation are a better fit for the data. 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.