The use of copulas to model non-Gaussian distributed multivariate data

Időpont: 
2019. 01. 16. 14:15
Hely: 
BME H. épület 306-os terem
Előadó: 
Krzysztof Domino Institute of Theoretical and Applied Informatics, PAS, Gliwice

 

                                     MEGHÍVÓ

           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.