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Mutual information-based approach for vine copula selection for hydrological dependence modeling
Published in Chongfu Huang, Zoe Nivolianitou, Risk Analysis Based on Data and Crisis Response Beyond Knowledge, 2019
Lingling Ni, Dong Wang, Jianfeng Wu
Copulas have been a natural choice, because they are flexible for constructing multivariate distribution by separating the construction into univariate marginal distributions and inter-dependence structure (Nelsen, 2006). As a result, there has been a flurry of applications of multivariate analysis in hydrology. Although copulas are flexible in dependence modeling, building higher-dimensional copulas is generally a difficult task (Aas et al., 2009; Hao and Singh, 2016). A d-dimensional copula is constructed using a set of d(d-1)/2 bivariate copulas sequentially in constructing conditional distributions which constitutes the vine copula (or pair copula construction) (Joe, 2014). From this point of view, vine copulas are hierarchical models as they sequentially apply bivariate copulas as the building blocks for constructing a higher-dimensional copula. The higher flexibility of vine copulas enables to model a wider range of complex multivariate dependence than other traditional copulas. Recently, vine copulas have been used in hydrological studies on frequency analysis (Xiong et al., 2014), flood characterization (Daneshkhah et al., 2016), rainfall simulation (Gyasi-Agyei and Melching, 2012), and streamflow prediction (Liu et al., 2015).
Modelling default dependence in automotive supply networks using vine-copula
Published in International Journal of Production Research, 2019
Therefore, one would recognise that the defaults propagation in the supply network of the automotive industry is a multifaceted problem. At one hand, car manufacturers operate in different countries and source their parts from different suppliers (cf. Kleindorfer and Saad 2005). They also engage in financial transactions, such as currency- and credit default swaps, with other car manufacturers. Thus, their failure would propagate horizontally and downwards, as pointed out in Wagner, Bode, and Koziol (2009) and Mizgier, Wagner, and Holyst (2012). On the other hand, parts suppliers also source for different car manufacturers, as well as competing with each others (cf. Wagner, Bode, and Koziol 2011). Therefore, it is fair to argue that while the results provided in Wagner, Bode, and Koziol (2009, 2011) and Mizgier, Wagner, and Holyst (2012) are valid, they, each, only paint a part of the full picture. This, strongly, motivates the use of vine-copula models to consider the entirety of the supply chain network simultaneously. From the statistical point of view, also, vine-copula are shown to be more versatile than copula models. For instance, the multivariate Gaussian copula is very restrictive and cannot account for features like asymmetry and heavy tails. Moreover, multivariate copulae, such as the multivariate Gaussian or Student-t, as well as exchangeable Archimedean copulae, lack the flexibility of accurately modelling the dependence among larger numbers of variables. Generalisations of these offer some improvement, but typically become rather conditional correlation intricate in their structure and, hence, exhibit other limitations such as parameter restrictions.