  We introduce an extension of R-vine copula models for the purpose of spatial
dependency modeling and model based prediction at unobserved locations. The
newly derived spatial R-vine model combines the flexibility of vine copulas
with the classical geostatistical idea of modeling spatial dependencies by
means of the distances between the variable locations. In particular the model
is able to capture non-Gaussian spatial dependencies. For the purpose of model
development and as an illustration we consider daily mean temperature data
observed at 54 monitoring stations in Germany. We identify a relationship
between the vine copula parameters and the station distances and exploit it in
order to reduce the huge number of parameters needed to parametrize a
54-dimensional R-vine model needed to fit the data. The new distance based
model parametrization results in a distinct reduction in the number of
parameters and makes parameter estimation and prediction at unobserved
locations feasible. The prediction capabilities are validated using adequate
scoring techniques, showing a better performance of the spatial R-vine copula
model compared to a Gaussian spatial model.

Methodology