Common sampling orders of regular vines with application to model selection

The selection of vine structure to represent dependencies in a data set with a regular vine copula model is still an open question. Up to date, the most popular heuristic to choose the vine structure is to construct consecutive trees by capturing largest correlations in lower trees. However, this might not lead to the optimal vine structure. A new heuristic based on sampling orders implied by regular vines is investigated. The idea is to start with an initial vine structure, that can be chosen with any existing procedure and search for a regular vine copula representing the data better within vines having 2 common sampling orders with this structure. Several algorithms are proposed to support the new heuristic. Both in the simulation study and real data analysis, the potential of the new heuristic to find a structure fitting the data better than the initial vine copula model, is shown.