R-vine models for spatial time series with an application to daily mean temperature.

We introduce an extension of R-vine copula models to allow for spatial dependencies and model based prediction at unobserved locations. The proposed spatial R-vine model combines the flexibility of vine copulas with the classical geostatistical idea of modeling spatial dependencies using the distances between the variable locations. In particular, the model is able to capture non-Gaussian spatial dependencies. To develop and illustrate our approach, we consider daily mean temperature data observed at 54 monitoring stations in Germany. We identify relationships between the vine copula parameters and the station distances and exploit these in order to reduce the huge number of parameters needed to parametrize a 54-dimensional R-vine model fitted to 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.