Pair-copula constructions of multiple dependence

By Kjersti Aas, Claudia Czado, Arnoldo Frigessi, Henrik Bakken. 2009

2,141 citations recorded by the source corpus.

Building on the work of Bedford, Cooke and Joe, we show how multivariate data, which exhibit complex patterns of dependence in the tails, can be modelled using a cascade of pair-copulae, acting on two variables at a time. We use the pair-copula decomposition of a general multivariate distribution and propose a method for performing inference. The model construction is hierarchical in nature, the various levels corresponding to the incorporation of more variables in the conditioning sets, using pair-copulae as simple building blocks. Pair-copula decomposed models also represent a very flexible way to construct higher-dimensional copulae. We apply the methodology to a financial data set. Our approach represents the first step towards the development of an unsupervised algorithm that explores the space of possible pair-copula models, that also can be applied to huge data sets automatically.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/817b6512d3d07ae231d525c366f9a95aa9bdc75a

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Citations in the corpus

A continuous rainfall model based on vine copulas (2015, positive): “Kurowicka and Cooke (2007); Aas et al. (2009); Aas and Berg (2009); Hobæk Haff et al. (2010)). The underlying theory for this method is 80 given by Bedford and Cooke (2001, 2002) and stems from Joe (1997), which also forms the basis for the method of “conditional mixtures", as applied by De Michele ”
Factor Copula Models for Replicated Spatial Data (2015, methodology): “Alternatively, one may use vine copula models, the joint distribution of which is constructed using bivariate, conditional linking copulas, including models with general structures, R-vines, and special cases such as C-vines; see Kurowicka and Cooke (2006) and Aas et al. (2009) for details.”
Maximum likelihood estimation of mixed C-vines with application to exchange rates (2012, methodology): “Aas et al. (2009) have shown that there are exactly d!”
Modelling skewed spatial random fields through the spatial vine copula (2014, methodology): “The vine copula estimation proceeds sequentially by using the best fitting copula per bivariate pair (details are provided in Aas et al. (2009), Czado et al.”
Selection of Vine Copulas (2013, methodology): “The article by [1] illustrates a first application of the vine copula concept using non-Gaussian pair copulas to financial data.”
A multivariate conditional model for streamflow prediction and spatial precipitation refinement (2015, methodology): “According to Joe [1996] and Aas et al. [2009], the conditional distribution functions F(x|ν) for an m-dimensional vector ν= (v1,.”
Hierarchies of Archimedean copulas (2010, methodology): “Aas et al. (2007) suggest a paircopula construction to model multivariate dependence in a flexible way. Berg and Aas (2007) compare pair-copula models with nested Archimedean copulas. An overview of many other methods for building multivariate copulas is given by Fischer and Köck (2007). In this pap”
Copulas in Econometrics (2014, methodology): “The decomposition of a joint density into the product of the marginal densities and the copula density, as in equation (1), reveals a convenient decomposition of the joint log-likelihood:”