Model selection for discrete regular vine copulas

Abstract Discrete vine copulas, introduced by Panagiotelis et al. (2012), provide a flexible modeling framework for high-dimensional data and have significant computational advantages over competing methods. A vine-based multivariate probability mass function is constructed from bivariate copula building blocks and univariate marginal distributions. However, even for a moderate number of variables, the number of alternative vine decompositions is very large and additionally there is a large set of candidate bivariate copulas that can be used as building blocks in any given decomposition. Together, these two issues ensure that it is infeasible to evaluate all possible vine copula models. In this paper we introduce two greedy algorithms for automatically selecting vine structures and component pair copula building blocks. The algorithms are tested in a simulation study that is itself driven by real world data from online retail. We show that both algorithms select vines that provide accurate estimates of the joint probabilities. Although the vine copulas selected are not exactly the same as the ‘true’ model in simulation studies, they are statistically indistinguishable from the true model according to the closeness test of Vuong (1989). Our algorithms outperform a Gaussian copula benchmark, especially for data with high dependence and also when predicting low probability tail events. Finally, we show that our selection algorithms outperform a Gaussian copula benchmark for data from the General Social Survey both in-sample and out-of-sample.