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

Kovács, Edith, and Szántai, Tamás. "On the connection between cherry-tree copulas and truncated R-vine copulas." Kybernetika 53.3 (2017): 437-460. <http://eudml.org/doc/294856>.

@article{Kovács2017,
abstract = {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 fastly 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-copulas and a lower number of conditional pair-copulas. In our earlier papers we introduced the concept of cherry-tree copulas. In this paper we characterize the relation between cherry-tree copulas and truncated R-vine copulas. It turns out that the concept of cherry-tree copula is more general than the concept of truncated R-vine copula. Although both contain in their expressions conditional independences between the variables, the truncated R-vines constructed in greedy way do not exploit the existing conditional independences in the data. We give a necessary and sufficient condition for a cherry-tree copula to be a truncated R-vine copula. We introduce a new method for truncated R-vine modeling. The new idea is that in the first step we construct the top tree by exploiting conditional independences for finding a good-fitting cherry-tree of order $k$. If this top tree is a tree in an R-vine structure then this will define a truncated R-vine at level $k$ and in the second step we construct a sequence of trees which leads to it. If this top tree is not a tree in an R-vine structure then we can transform it into such a tree at level $k+1$ and then we can again apply the second step. The second step is performed by a backward construction named Backward Algorithm. This way the cherry-tree copulas always can be expressed by pair-copulas and conditional pair-copulas.},
author = {Kovács, Edith, Szántai, Tamás},
journal = {Kybernetika},
keywords = {copula; conditional independences; Regular-vine; truncated vine; cherry-tree copula},
language = {eng},
number = {3},
pages = {437-460},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the connection between cherry-tree copulas and truncated R-vine copulas},
url = {http://eudml.org/doc/294856},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Kovács, Edith
AU - Szántai, Tamás
TI - On the connection between cherry-tree copulas and truncated R-vine copulas
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 3
SP - 437
EP - 460
AB - 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 fastly 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-copulas and a lower number of conditional pair-copulas. In our earlier papers we introduced the concept of cherry-tree copulas. In this paper we characterize the relation between cherry-tree copulas and truncated R-vine copulas. It turns out that the concept of cherry-tree copula is more general than the concept of truncated R-vine copula. Although both contain in their expressions conditional independences between the variables, the truncated R-vines constructed in greedy way do not exploit the existing conditional independences in the data. We give a necessary and sufficient condition for a cherry-tree copula to be a truncated R-vine copula. We introduce a new method for truncated R-vine modeling. The new idea is that in the first step we construct the top tree by exploiting conditional independences for finding a good-fitting cherry-tree of order $k$. If this top tree is a tree in an R-vine structure then this will define a truncated R-vine at level $k$ and in the second step we construct a sequence of trees which leads to it. If this top tree is not a tree in an R-vine structure then we can transform it into such a tree at level $k+1$ and then we can again apply the second step. The second step is performed by a backward construction named Backward Algorithm. This way the cherry-tree copulas always can be expressed by pair-copulas and conditional pair-copulas.
LA - eng
KW - copula; conditional independences; Regular-vine; truncated vine; cherry-tree copula
UR - http://eudml.org/doc/294856
ER -