pyvine: The Python Package for Regular Vine Copula Modeling, Sampling and Testing

• Published in: Communications in mathematics and statistics Vol. 9; no. 1; pp. 53 - 86
• Main Authors: Yuan, Zhenfei, Hu, Taizhong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2021; Springer Nature B.V
• Subjects: Algorithms; Bivariate analysis; Dependence; Distribution functions; Goodness of fit; Mathematics; Mathematics and Statistics; Maximum likelihood estimation; Optimization; Overflow; Sampling; Statistical analysis; Statistical methods; Statistics; Regular vine copula; Bivariate copula; Multivariate modeling; Multivariate sampling; 62H20; Rosenblatt’s transformation; Anderson–Darling test; Dependence structure; 62E17
• ISSN: 2194-6701; 2194-671X
• DOI: 10.1007/s40304-019-00195-2

Regular vine copula provides rich models for dependence structure modeling. It combines vine structures and families of bivariate copulas to construct a number of multivariate distributions that can model a wide range dependence patterns with different tail dependence for different pairs. Two special cases of regular vine copulas, C-vine and D-vine copulas, have been extensively investigated in the literature. We propose the Python package, pyvine , for modeling, sampling and testing a more generalized regular vine copula (R-vine for short). R-vine modeling algorithm searches for the R-vine structure which maximizes the vine tree dependence in a sequential way. The maximum likelihood estimation algorithm takes the sequential estimations as initial values and uses L-BFGS-B algorithm for the likelihood value optimization. R-vine sampling algorithm traverses all edges of the vine structure from the last tree in a recursive way and generates the marginal samples on each edge according to some nested conditions. Goodness-of-fit testing algorithm first generates Rosenblatt’s transformed data E and then tests the hypothesis H 0 ∗ : E ∼ C ⊥ by using Anderson–Darling statistic, where C ⊥ is the independence copula. Bootstrap method is used to compute an adjusted p -value of the empirical distribution of replications of Anderson–Darling statistic. The computing of related functions of copulas such as cumulative distribution functions, H-functions and inverse H-functions often meets with the problem of overflow. We solve this problem by reinvestigating the following six families of bivariate copulas: Normal, Student t , Clayton, Gumbel, Frank and Joe’s copulas. Approximations of the above related functions of copulas are given when the overflow occurs in the computation. All these are implemented in a subpackage bvcopula , in which subroutines are written in Fortran and wrapped into Python and, hence, good performance is guaranteed.