StructureSelect (VineCopulaObject)
Selecting the structure and pair-copula families for a vine copula
Purpose
The function can be used to find an adequate structure and to select pair-copula families for a given data set. By default (StructuringRule = 0) the nodes of the C-vine are chosen in a way that in each tree, the root (i.e. the node, which is connected by a copula to all other nodes) is the variable which has maximal dependence with all other variables. The maximal dependence is found by choosing the variable which has the maximal column sum in the matrix of absolute empirical Kendall’s τ (cf. Schepsmeier, Stöber, and Brechmann (2013) for an R-function (RVineStructureSelect) of exactly the same procedure and Czado, Schepsmeier, and Min (2012, p. 240) for the theoretical background of the approach).
Alternative methods for choosing a structure for C-Vine copulas (cf. Nikoloulopoulos, Joe and Li (2012)): The root node of the first tree is chosen in the same way as in the default method, i.e., the variable with the strongest dependence with all other variables. Then one can choose between three rules suggested in Nikoloulopoulos, Joe and Li (2012, p.3665): StructuringRule = 1: List the other variables by their dependence to the root node in decreasing order. StructuringRule = 2: List the other variables by their dependence to the root node in increasing order. StructuringRule = 3: List the other variables sequentially by choosing the variable which is least dependent with the previously selected one.
Furthermore, the copula families are chosen according to the AIC criterion and for each pair- copula an independence test is performed (cf. Schepsmeier, Stöber, and Brechmann (2013) and Brechmann and Schepsmeier (2013) for R-functions (RVineStructureSelect / RVineCopSelect / CDVineCopSelect) and Genest and Favre (2007, p. 351) for the independence test).
For D-Vine copulas there is no structuring rule implemented yet. Therefore, the function uses the specified structure and only selects the pair-copula families using the AIC criterion.
Usage
Select a simplified vine copula model
VineCopulaHat = StructureSelect(VineCopulaObject,u)
Select a simplified vine copula model, where the
pair-copulas are from a specified set of families
(possible choices 'all' (default), 'R', 'R-package',
'VineCopulaPackage' (they all are equivalent and
correspond to the set of pair-copulas of the R-package
VineCopula (Schepsmeier, Stöber, and Brechmann (2013),
Version 1.2)) or a cell-array consisting of possible
pair-copula families (i.e., a user selected list of
possible pair-copula families).
VineCopulaHat = StructureSelect(VineCopulaObject,u,'all')
VineCopulaHat = StructureSelect(VineCopulaObject,u,'R')
VineCopulaHat = StructureSelect(VineCopulaObject,u,'R-package')
VineCopulaHat = StructureSelect(VineCopulaObject,u,'VineCopulaPackage')
VineCopulaHat = StructureSelect(VineCopulaObject,u,familyset)
Select a simplified vine copula model using an
alternative structuring rule:
VineCopulaHat = StructureSelect(VineCopulaObject,u,familyset,1)
VineCopulaHat = StructureSelect(VineCopulaObject,u,familyset,2)
VineCopulaHat = StructureSelect(VineCopulaObject,u,familyset,3)
Inputs
VineCopulaObject= An object from the class VineCopula.
u = A (n x d) dimensional vector of
values lying in [0,1] (the
observations).
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
array containing a subset of the
possible families:
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
Outputs
VineCopulaHat = An object from the class VineCopula.
The selected vine copula structure can
be found in VineCopulaHat.structure
and the selected pair-copulas in
VineCopulaHat.families. Furthermore,
the sequential estimates, which are
obtained during the selection
procedure of the structure and
copula families, are stored in
VineCopulaHat.parameters.
References
[1] Brechmann, E. C. and U. Schepsmeier (2013), "Modeling Dependence with C- and D-Vine Copulas: The R-Package CDVine", Journal of Statistical Software 52(3), R package version 1.1-13, pp. 1-27, url: http://CRAN.R-project.org/package=CDVine.
[2] Czado, C., U. Schepsmeier, and A. Min (2012), "Maximum likelihood estimation of mixed C-vines with application to exchange rates", Statistical Modelling 12(3), pp. 229-255.
[3] Genest, C. and A. Favre (2007), "Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask", Journal of Hydrologic Engineering 12(4), pp. 347- 368.
[4] Nikoloulopoulos, A. K., H. Joe, H. Li (2012), "Vine copulas with asymmetric tail dependence and applications to financial return data", Computational Statistics & Data Analysis 56(11), pp. 3659-3673.
[5] 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.