Title: Time varying graphs
Authors: Matteo Iacopini - Vrije Universiteit Amsterdam (Netherlands) [presenting]
Dominique Guegan - Universite Paris 1 - Pantheon-Sorbonne (France)
Abstract: A method is proposed to study the dynamics of the dependence relation among a set of random variables, whose conditional independence relationships can be described by means of a graph. The procedure consists in five steps and exploits Vine Copula for representing the joint density of the set of RVs at each time, then a suitable invertible transformation is applied to map this distribution function into a tractable new space. The dynamics is introduced by defining and estimating an autoregressive process in this space, with the aim of making a one step ahead forecast. Finally, the invertibility of the transformation allows to obtain the predicted copula. The resulting distribution can be directly studied (global approach) by means of the relevant statistics; in addition, we would propose a way to infer the corresponding change of the graphical structure (specific approach). The method we propose is almost nonparametric, proving high flexibility in modeling the dependence relations among RVs, while a simple AR process is dened for modeling time variation, which facilitate the interpretation without constraining.