Flexible multivariate statistical dependence models are needed for many=20 data structures. While the popular multivariate normal distribution is=20 very restrictive and cannot account for features like asymmetry and=20 heavy tails, copulas can be used to build more flexible models.=20 Exploiting the famous theorem by Sklar which allows to separate the=20 dependence structure from the marginal distributions many successful=20 models have been developed in recent years. Much of this research=20 however is limited to the bivariate case, where numerous copulas are=20 available. This is unlike the multivariate case, where standard=20 multivariate copulas are rather restrictive in their structure. Vine=20 copulas do not suffer from such shortcomings and can be conveniently=20 constructed using only bivariate copulas as building blocks. In this=20 talk I introduce the concept of vine copulas and discuss appropriate=20 statistical inference techniques. This in particular includes issues of=20 model selection, which may be challenging in higher dimensions. As an=20 application I consider weather measurements of different variables like=20 temperature, humidity and pressure observed at Hohenpeissenberg, the=20 oldest mountain weather station in the world. Finally, I give an outlook=20 how such models may be extended to data from multiple stations using a=20 hierarchical copula construction.
Joint work with Michael Pachali, Claudia Czado, and Christian Zang.