CDVineCondFit {CDVineCopulaConditional}R Documentation

Selection of a C- or D- vine copula model for conditional sampling


This function fits either a C- or a D- vine model to a d-dimensional dataset of uniform variables. The fit of the pair-copula families is performed sequentially through the function RVineCopSelect of the package VineCopula. The vine structure is selected among a group of C- and a D- vines which satisfy the requirement discussed in Bevacqua et al. (2017). This group is composed by all C- and D- vines from which the conditioning variables would be sampled as first when following the algorithms from Aas et al. (2009). Alternatively, if the vine matrix describing the vine structure is given to the function, the fit of the pair-copulas is directly performed skipping the vine structure selection procedure.


CDVineCondFit(data, Nx, treecrit = "AIC", type = "CVine-DVine",
  selectioncrit = "AIC", familyset = NA, indeptest = FALSE,
  level = 0.05, se = FALSE, rotations = TRUE, method = "mle",
  Matrix = FALSE)



An N x d data matrix (with uniform margins). The data of the conditioning variable(s) have to occupy the last column(s) of this matrix.


Number of conditioning variables.


Character indicating the criteria used to select the vine. All possible vines are fitted trough the function RVineCopSelect of the package VineCopula. Then the vines are ranked with respect the Akaike information criterion (treecrit = "AIC", default) or Bayesian information criterion (treecrit = "BIC"). This need the estimation and model selection for all the pairs of all the possible vines, therefore could require long time in case of large datasets, i.e. large N x d.


Type of vine to be fitted:
C-Vine: "CVine" or 1;
D-Vine: "DVine" or 2;
Both C and D-Vine: "CVine-DVine" or "1-2" (default).


Character indicating the criterion for pair-copula selection. Possible choices are "AIC" (default) and "BIC".


"Integer vector of pair-copula families to select from. The vector has to include at least one pair-copula family that allows for positive and one that allows for negative dependence. Not listed copula families might be included to better handle limit cases. If familyset = NA (default), selection among all possible families is performed. If a vector of negative numbers is provided, selection among all but abs(familyset) is performed. Coding of bivariate copula families:
0 = independence copula
1 = Gaussian copula
2 = Student t copula (t-copula)
3 = Clayton copula
4 = Gumbel copula
5 = Frank copula
6 = Joe copula
7 = BB1 copula
8 = BB6 copula
9 = BB7 copula
10 = BB8 copula
13 = rotated Clayton copula (180 degrees; “survival Clayton”)
14 = rotated Gumbel copula (180 degrees; “survival Gumbel”)
16 = rotated Joe copula (180 degrees; “survival Joe”)
17 = rotated BB1 copula (180 degrees; “survival BB1”)
18 = rotated BB6 copula (180 degrees; “survival BB6”)
19 = rotated BB7 copula (180 degrees; “survival BB7”)
20 = rotated BB8 copula (180 degrees; “survival BB8”)
23 = rotated Clayton copula (90 degrees)
24 = rotated Gumbel copula (90 degrees)
26 = rotated Joe copula (90 degrees)
27 = rotated BB1 copula (90 degrees)
28 = rotated BB6 copula (90 degrees)
29 = rotated BB7 copula (90 degrees)
30 = rotated BB8 copula (90 degrees)
33 = rotated Clayton copula (270 degrees)
34 = rotated Gumbel copula (270 degrees)
36 = rotated Joe copula (270 degrees)
37 = rotated BB1 copula (270 degrees)
38 = rotated BB6 copula (270 degrees)
39 = rotated BB7 copula (270 degrees)
40 = rotated BB8 copula (270 degrees)
104 = Tawn type 1 copula
114 = rotated Tawn type 1 copula (180 degrees)
124 = rotated Tawn type 1 copula (90 degrees)
134 = rotated Tawn type 1 copula (270 degrees)
204 = Tawn type 2 copula
214 = rotated Tawn type 2 copula (180 degrees)
224 = rotated Tawn type 2 copula (90 degrees)
234 = rotated Tawn type 2 copula (270 degrees)


Logical; whether a hypothesis test for the independence of u1 and u2 is performed before bivariate copula selection (default: indeptest = FALSE; see BiCopIndTest). The independence copula is chosen for a (conditional) pair if the null hypothesis of independence cannot be rejected.


numeric; significance level of the independence test (default: level = 0.05).


Logical; whether standard errors are estimated (default: se = FALSE).


logical; if TRUE, all rotations of the families in familyset are included.


indicates the estimation method: either maximum likelihood estimation (method = "mle"; default) or inversion of Kendall's tau (method = "itau"). For method = "itau" only one parameter families and the Student t copula can be used (family = 1,2,3,4,5,6,13,14,16,23,24,26,33,34 or 36). For the t-copula, par2 is found by a crude profile likelihood optimization over the interval (2, 10]." (VineCopula Documentation, version 2.1.1, pp. 73-75)


d x d matrix that defines the vine structure. If Matrix is not given, the routine finds the best vine structure according to selectioncrit. If Matrix is given, the fit is performed only if the structure respects the necessary conditions for the conditional sampling (if the conditions are not respected, an error message is returned).


An RVineMatrix object describing the selected copula model (for further details about RVineMatrix objects see the documentation file of the VineCopula package). The selected families are stored in $family, and the sequentially estimated parameters in $par and $par2. The fit of the model is performed via the function RVineCopSelect of the package VineCopula.

"The object RVineMatrix includes the following information about the fit:

se, se2

standard errors for the parameter estimates (if se = TRUE; note that these are only approximate since they do not account for the sequential nature of the estimation,


number of observations,

logLik, pair.logLik

log likelihood (overall and pairwise)

AIC, pair.AIC

Aikaike's Informaton Criterion (overall and pairwise),

BIC, pair.BIC

Bayesian's Informaton Criterion (overall and pairwise),


matrix of empirical values of Kendall's tau,


matrix of p-values of the independence test.


For a comprehensive summary of the vine copula model, use summary(object); to see all its contents, use str(object)". (VineCopula Documentation, version 2.1.1, pp. 103)


Emanuele Bevacqua


Bevacqua, E., Maraun, D., Hobaek Haff, I., Widmann, M., and Vrac, M.: Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy), Hydrol. Earth Syst. Sci., 21, 2701-2723,, 2017. [link] [link]

Aas, K., Czado, C., Frigessi, A. and Bakken, H.: Pair-copula constructions of multiple dependence, Insurance: Mathematics and Economics, 44(2), 182-198, <doi:10.1016/j.insmatheco.2007.02.001>, 2009. [link]

Ulf Schepsmeier, Jakob Stoeber, Eike Christian Brechmann, Benedikt Graeler, Thomas Nagler and Tobias Erhardt (2017). VineCopula: Statistical Inference of Vine Copulas. R package version 2.1.1. [link]

See Also

CDVineCondSim, CDVineCondRank


# Example 1

# Read data 
data <- dataset$data[1:100,1:5]

# Define the variables Y and X. X are the conditioning variables, 
# which have to be positioned in the last columns of the data.frame
colnames(data) <- c("Y1","Y2","X3","X4","X5")

## Not run: 
# Select and fit a C- vine copula model, requiring that the 
RVM <- CDVineCondFit(data,Nx=3,treecrit="BIC",type="CVine",selectioncrit="AIC")

## End(Not run)

# Example 2

# Read data 
data <- dataset$data[1:80,1:5]

# Define the variables Y and X. X are the conditioning variables, 
# which have to be positioned in the last columns of the data.frame
colnames(data) <- c("Y1","Y2","X3","X4","X5")

# Define a VineMatrix which can be used for conditional sampling
ListVines <- CDVineCondListMatrices(data,Nx=3)

## Not run: 
# Fit copula families for the defined vine:
RVM <- CDVineCondFit(data,Nx=3,Matrix=Matrix)

# check

# Fit copula families for the defined vine, given a group of families to select from:
RVM <- CDVineCondFit(data,Nx=3,Matrix=Matrix,familyset=c(1,2,3,14))

# Try to fit copula families for a vine which is not among those 
# that allow for conditional sampling:
RVM <- CDVineCondFit(data,Nx=3,Matrix=Matrix)

## End(Not run)

[Package CDVineCopulaConditional version 0.1.1 Index]