PairCopulaSelect

Selecting pair-copula families

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Purpose

The function selects pair-copula families by applying the test for independence of copula data of Genest and Favre (2007) using a significance level of 5 and afterwards, in the case of an rejection of the H0, it selects the "best" fitting pair-copula by optimizing with respect to Akaike's information criterion (AIC). The set of pair-copula families that are tested can be specified in several ways. By chosing the option 'all', the possible pair-copulas are:

       0   Indep
       1   AMH
       2   AsymFGM
       3   BB1
       4   BB6
       5   BB7
       6   BB8
       7   Clayton
       8   FGM
       9   Frank
       10  Gaussian
       11  Gumbel
       12  IteratedFGM
       13  Joe
       14  PartialFrank
       15  Plackett
       16  Tawn1
       17  Tawn2
       18  Tawn
       19  t

Alternatively, one can specify a own subset of copula families or one can choose the option 'R-package', which coincides with the pair-copula families set of the R-package VineCopula of Schepsmeier, Stöber, and Brechmann (2013). The possible rotation degrees for the rotatable pair-copula families are always choosen according to the empirical Kendall's tau values.

Usage

       Pair copula selection from the whole set of possible families
       (default).
   [family,ParamHat,rotation] = PairCopulaSelect(u1,u2)
   [family,ParamHat,rotation] = PairCopulaSelect(u1,u2,'all')
       Pair copula selection from a user specified set of possible
       pair-copula families.
   [family,ParamHat,rotation] = PairCopulaSelect(u1,u2,familyset)
       Pair copula selection from the set of pair-copula families,
       which coincides with the one of the  R-package VineCopula of
       (cf. Schepsmeier, Stöber, and Brechmann (2013)), where the
       following commands are all equivalent.
   [family,ParamHat,rotation] = PairCopulaSelect(u1,u2,'R')
   [family,ParamHat,rotation] = PairCopulaSelect(u1,u2,'R-package')
   [family,ParamHat,rotation] = PairCopulaSelect(u1,u2,'VineCopulaPackage')

Inputs

   u1        = A (n x 1) dimensional vector of values lying in [0,1].
   u2        = A (n x 1) dimensional vector of values lying in [0,1].
   familyset = The set of possible pair-copula families. By setting it
               to the strings 'all', 'R', 'R-package' or
               'VineCopulaPackage' one can choose one of the pre-
               defined sets. Alternatively, one can choose an vector
               containing a subset of the possible families.

Outputs

   family    = The selected pair-copula family.
   ParamHat  = The maximum-likelihood estimates for the parameters of
               the selected pair-copula family.
   rotation  = The selected rotation level (can of course be empty).

References

Schepsmeier, U., J. Stöber and E. C. Brechmann (2013), VineCopula: Statistical inference of vine copulas, R package version 1.2, url: http://CRAN.R-project.org/package=VineCopula.