Szeretettel meghívjuk Krzysztof Domino előadására
az Optimalizálási Szeminárium keretében
2019. január 16-án szerdán, 14:15-15:45 óráig
Helyszín: BME H épület H. 306 terem
Előadó: Krzysztof Domino, Institute of Theoretical and Applied Informatics, PAS, Gliwice
The use of copulas to model non-Gaussian distributed multivariate data
Abstract: The goal of this talk is to discuss non-Gaussian multivariate probabilistic models based on copulas. One of most sound examples of non-Gaussian multivariate data are financial data. For the practical example, during the crisis there appear simultaneous extreme drops in many assets values. These can not by modeled by multivariate Gaussian distribution but by an adequate copula.
In the talk, we introduce copulas formally, discuss their features, basic families and mention relation between copulas and higher order multivariate statistics (cumulants). From the formal point of vies, we refer to theSklar's theorem, stating that any multivariate (joint) cumulative distribution function (CDF) can be express in terms of univariate marginal CDFs and the copula. Then we discuss basic copulas families, such as elliptical, Frechet, Archimedean and Marshall-Olkin.
Next we discuss the relation between copulas and higher order multivariate cumulants that are zero only for multivariate Gaussian distributed data, and can be potentially used in the copula selection procedure.