# On the connection between cherry-tree copulas and truncated R-vine copulas

arXiv: https://arxiv.org/abs/1604.03269 · HTML: https://mlsanity.com/paper/1604.03269/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Apr 2016.

## Built on by (most cited first, 2 of 2)

- [Trunc-Opt vine building algorithms](https://mlsanity.com/paper/2512.14399/) (2025)
- [Matrix and graph representations of vine copula structures](https://mlsanity.com/paper/2205.04783/) (2022)

## Abstract (arXiv)

Vine copulas are a flexible way for modeling dependences using only pair-copulas as building blocks. However if the number of variables grows the problem gets fast intractable. For dealing with this problem Brechmann at al. proposed the truncated R-vine copulas. The truncated R-vine copula has the very useful property that it can be constructed by using only pair-wise copulas, and conditional pair-wise copulas. In our earlier papers we introduced the concept of cherry-tree copulas. In this paper we characterize the relation between the cherry-tree copulas and the truncated R-vine copulas. Both are based on exploiting of some conditional independences between the variables. We give a necessary and sufficient condition for a cherry-tree copula to be a truncated R-vine copula. We introduce a new perspective for truncated R-vine modeling. The new idea is finding first a good fitting cherry-tree copula of order k. Then, if this is also a truncated R-vine copula we apply the Backward Algorithm introduced in this paper. This way the construction of a sequence of trees which leads to it becomes possible. So the cherry-tree copula can be expressed by pair-copulas and conditional pair-copulas. In the case when the fitted k order cherry-tree copula is not a truncated R-vine copula we give an algorithm to transform it into truncated R-vine copula at level k+1. Therefore this cherry-tree copula can also be expressed by pair-copulas.