Spatial composite likelihood inference using local C-vines

TL;DR

This paper introduces a novel spatial dependency modeling method using local C-vine copulas within a composite likelihood framework, enabling flexible, non-Gaussian dependency capture and spatial prediction.

Contribution

It develops the spatial local C-vine composite likelihood (S-LCVCL) method, combining geostatistics and copula models for improved spatial dependency analysis.

Findings

Outperforms existing spatial dependency models in temperature data prediction

Effectively captures non-Gaussian dependencies in spatial data

Validated using temperature data from Germany with superior predictive scores

Abstract

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 Comparison with two other approaches of spatial dependency modeling introduced in yet unpublished work of Erhardt, Czado and Schepsmeier (2014) shows a preference for the local C-vine composite likelihood approach.