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

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,Hfunctions 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.