Modelling skewed spatial random fields through the spatial vine copula

Abstract

Studying phenomena that follow a skewed distribution and entail an extremal behaviour is important in many disciplines. How to describe and model the dependence of skewed spatial random fields is still a challenging question. Especially when one is interested in interpolating a sample from a spatial random field that exhibits extreme events, classical geostatistical tools like kriging relying on the Gaussian assumption fail in reproducing the extremes. Originating from the multivariate extreme value theory partly driven by financial mathematics, copulas emerged in recent years being capable of describing different kinds of joint tail behaviours beyond the Gaussian realm. In this paper spatial vine copulas are introduced that are parametrized by distance and allow to include extremal behaviour of a spatial random field. The newly introduced distributions are fitted to the widely studied emergency and routine scenario data set from the spatial interpolation comparison 2004 (SIC2004). The presented spatial vine copula ranks within the top 5 approaches and is superior to all approaches in terms of the mean absolute error.