A non-stationary factor copula model for non-Gaussian spatial data

We introduce a new copula model for non-stationary replicated spatial data. It is based on the assumption that a common factor exists that controls the joint dependence of all the observations from the spatial process. As a result, our proposal can model tail dependence and tail asymmetry, unlike the Gaussian copula model. Moreover, we show that the new model can cover a full range of dependence between tail quadrant independence and tail dependence. Although the log-likelihood of the model can be obtained in a simple form, we discuss its numerical computational issues and ways to approximate it for drawing inference. Using the estimated copula model, the spatial process can be interpolated at locations where it is not observed. We apply the proposed model to temperature data over the western part of Switzerland, and we compare its performance with that of its stationary version and with the Gaussian copula model.