2016/04/12 by Edith Kovács, Kovács, Edith, Tamás Szántai +1 · 1 citation
Economics, Econometrics and Finance · #60C05 #62H05 #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME)
paper · pdf · doi:10.48550/arxiv.1604.03269
openalex publication_date 2016/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Vine copulas are a flexible way for modeling dependences using only\npair-copulas as building blocks. However if the number of variables grows the\nproblem gets fast intractable. For dealing with this problem Brechmann at al.\nproposed the truncated R-vine copulas. The truncated R-vine copula has the very\nuseful property that it can be constructed by using only pair-wise copulas, and\nconditional pair-wise copulas. In our earlier papers we introduced the concept\nof cherry-tree copulas. In this paper we characterize the relation between the\ncherry-tree copulas and the truncated R-vine copulas. Both are based on\nexploiting of some conditional independences between the variables. We give a\nnecessary and sufficient condition for a cherry-tree copula to be a truncated\nR-vine copula. We introduce a new perspective for truncated R-vine modeling.\nThe new idea is finding first a good fitting cherry-tree copula of order k.\nThen, if this is also a truncated R-vine copula we apply the Backward Algorithm\nintroduced in this paper. This way the construction of a sequence of trees\nwhich leads to it becomes possible. So the cherry-tree copula can be expressed\nby pair-copulas and conditional pair-copulas. In the case when the fitted k\norder cherry-tree copula is not a truncated R-vine copula we give an algorithm\nto transform it into truncated R-vine copula at level k+1. Therefore this\ncherry-tree copula can also be expressed by pair-copulas.\n