Modelling skewed spatial random fields through the spatial vine copula

By Benedikt Gräler. 2014

113 citations recorded by the source corpus.

a b s t r a c t Studying phenomena that follow a skewed distribution and entail an extremal behaviour is important in many disciplines. How to describe and model the dependence of skewed spatial random fields is still a challenging question. Especially when one is interested in interpolating a sample from a spatial random field that exhibits extreme events, classical geostatistical tools like kriging relying on the Gaussian assumption fail in reproducing the extremes. Originating from the multivariate extreme value theory partly driven by financial mathematics, copulas emerged in recent years being capable of describing different kinds of joint tail behaviours beyond the Gaussian realm. In this paper spatial vine copulas are introduced that are parametrized by distance and allow to include extremal behaviour of a spatial random field. The newly introduced distributions are fitted to the widely studied emergency and routine scenario data set from the spatial interpolation comparison 2004 (SIC2004). The presented spatial vine copula ranks within the top 5 approaches and is superior to all approaches in terms of the mean absolute error.

Subfields: Economics and Econometrics, Environmental Engineering, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/e7a3b2d7e737141b4f83ba9c1d1dbfcdd4d2c25a

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Citations in the corpus

A continuous rainfall model based on vine copulas (2015, unknown): “The use of vine copulas is becoming popular in ﬁnance (see e.g. Nikololoupoulos et al. (2012); Zhang (2014); Mendes and Accioly (2014)) and geophysics and hydrology (see e.g. Gräler (2014); Xiong et al. (2014); Gyasi-Agyei and Melch-ing (2012); Gräler et al. (2013)).”
Factor Copula Models for Replicated Spatial Data (2015, methodology): “To achieve greater flexibility, different copula families and convex combinations may be used; see Gräler and Pebesma (2011) and Gräler (2014).”
Modeling the spatial dependence of floods using the Fisher copula (2019, methodology): “…(Ghizzoni et al., 2010, 2012), max-stable models (Wang et al., 2014), and copula models such as pair-copula constructions (Bevacqua et al., 2017; Gräler, 2014; Schulte and Schu-mann, 2015), hierarchical Kendall copulas (Fischer et al., 2017), and factor copula models (Lee and Joe, 2017).”
Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model (2016, background): “The conditional distributions/expectations at lower levels of a deeper pair-copula model must then be estimated based on fewer data points which can be then less accurate and noisier (see also Gräler (2014) reported a sort of similar problem in modeling extreme data using spatial vine copula).”
Random forest as a generic framework for predictive modeling of spatial and spatio-temporal variables (2018, methodology): “models based on copulas (Erhardt et al., 2015; Gräler, 2014), but these are 614 even more computational and cumbersome to implement on large datasets.”