| Title:
|
On the connection between cherry-tree copulas and truncated R-vine copulas (English) |
| Author:
|
Kovács, Edith |
| Author:
|
Szántai, Tamás |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
53 |
| Issue:
|
3 |
| Year:
|
2017 |
| Pages:
|
437-460 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
copula |
| Keyword:
|
conditional independences |
| Keyword:
|
Regular-vine |
| Keyword:
|
truncated vine |
| Keyword:
|
cherry-tree copula |
| MSC:
|
60C05 |
| MSC:
|
62H05 |
| idZBL:
|
Zbl 06819617 |
| idMR:
|
MR3684679 |
| DOI:
|
10.14736/kyb-2017-3-0437 |
| . |
| Date available:
|
2017-11-12T09:41:27Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/146936 |
| . |
| Reference:
|
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