Spatial composite likelihood inference using local C-vines

Abstract

We present a vine copula based composite likelihood approach to model spatial dependencies, which allows to perform prediction at arbitrary locations. It combines established methods to model (spatial) dependencies. On the one hand spatial differences between the variable locations are utilized to model the degree of spatial dependence. On the other hand the flexible class of C-vine copulas are used to model the spatial dependency structure locally. These local C-vine copulas are parametrized jointly, exploiting a relationship between the copula parameters and the corresponding spatial distances and elevation differences, and are combined in a composite likelihood approach. This spatial local C-vine composite likelihood (S-LCVCL) method benefits from the fact that it is able to capture non-Gaussian dependency structures. The development and validation of the new methodology is illustrated using a data set of daily mean temperatures observed at 73 observation stations spread over Germany. For validation continuous ranked probability scores are utilized. Comparison with another vine copula based approach and a Gaussian approach for spatial dependency modeling shows a preference for vine copula based (spatial) dependency structures.