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166. Introduction

Author

Tobias, Michael Charles, Morrison, Jane Gray, Tobias, Michael Charles, and Morrison, Jane Gray

Published
2019
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176. Choices

Author

Tobias, Michael Charles, Morrison, Jane Gray, Tobias, Michael Charles, and Morrison, Jane Gray

Published
2018
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187. Spatial composite likelihood inference using local C-vines

Author

Erhardt, Tobias Michael, Czado, Claudia, and Schepsmeier, Ulf

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 Comparison with two other approaches of spatial dependency modeling introduced in yet unpublished work of Erhardt, Czado and Schepsmeier (2014) shows a preference for the local C-vine composite likelihood approach.

Published
2014

188. R-vine Models for Spatial Time Series with an Application to Daily Mean Temperature

Author

Erhardt, Tobias Michael, Czado, Claudia, and Schepsmeier, Ulf

Subjects
Statistics - Methodology
Abstract

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., Comment: 28 pages, 10 figures

Published
2014

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