  We present a vine copula based composite likelihood approach to model spatial
dependencies, which allows to perform prediction at arbitrary locations. This
approach combines established methods to model (spatial) dependencies. On the
one hand the geostatistical concept utilizing spatial differences between the
variable locations to model the extend of spatial dependencies is applied. On
the other hand the flexible class of C-vine copulas is utilized to model the
spatial dependency structure locally. These local C-vine copulas are
parametrized jointly, exploiting an existing relationship between the copula
parameters and the respective spatial distances and elevation differences, and
are combined in a composite likelihood approach. The new methodology called
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 two other approaches of spatial dependency modeling introduced
in yet unpublished work of Erhardt, Czado and Schepsmeier (2014) shows a
preference for the local C-vine composite likelihood approach.
