The pair-copula construction in space and time: a new approach to model spatio-temporal dependencies

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Copulas are a statistical concept capable of modelling any kind of dependence between random variables detached from their margins. Capturing the non-Gaussian dependencies of extreme data made them popular in financial risk assessment. Non-Gaussian dependencies can also be found in many spatio-temporal datasets. In contrast to classical approaches, non-Gaussian and in particular asymmetric dependencies can easily be captured with copulas. Exploiting copulas improves the interpolation of skewed data. Furthermore, copulas enable us to assess the risk of extreme events. The concept of copulas is new to the domain of spatio-temporal Geostatistics. The challenge is to find a suitable copula that fits the dataset. In contrast to multivariate copulas, bivariate copulas are quite well understood and are naturally less complex. A very promising algorithm exploiting the simplicity of bivariate copulas and constructing multivariate ones is the pair-copula construction (PCC) which has been successfully applied to multivariate time series in finance. In the spatio-temporal context, a pair-copula’s dimension depends on the quantity of points involved. Likewise, the number of bivariate copulas building up the pair-copula will grow quadratic. To overcome this issue we will develop fast estimation procedures and smart algorithms reducing the number of pair-copulas to be estimated. Furthermore, we will implement the procedures in a self-sufficient manner to allow for an automated processing. The PCC will be compared with other recent approaches and applied to two use-cases.