VineCopula (version 1.0)

RVineHessian: Hessian matrix of the log-likelihood of an R-vine copula model

Description

This function calculates the Hessian matrix of the log-likelihood of a d-dimensional R-vine copula model with respect to the copula parameter and evaluates it on a given copula data set.

Usage

RVineHessian(data, RVM)

Arguments

data

An N x d data matrix (with uniform margins).

RVM

An RVineMatrix object including the structure, the pair-copula families, and the parameters.

Value

• hessian
  The calculated Hessian matrix of the log-likelihood value of the R-vine copula model.
• der
  The product of the gradient vector with its transposed version.

References

Schepsmeier, U. and J. Stoeber (2012). Derivatives and Fisher information of bivariate copulas. Submitted for publication. http://mediatum.ub.tum.de/node?id=1106541. Stoeber, J. and U. Schepsmeier (2012). Is there significant time-variation in multivariate dependence?. In preparation. http://de.arxiv.org/abs/1205.4841. Dissmann, J. F., E. C. Brechmann, C. Czado, and D. Kurowicka (2011). Selecting and estimating regular vine copulae and application to financial returns. Submitted for publication. http://mediatum.ub.tum.de/node?id=1079277

See Also

BiCopDeriv, BiCopDeriv2, BiCopHfuncDeriv, BiCopHfuncDeriv2, RVineMatrix, RVineMLE, RVineGrad

Examples

# define 5-dimensional R-vine tree structure matrix
Matrix = c(5,2,3,1,4,0,2,3,4,1,0,0,3,4,1,0,0,0,4,1,0,0,0,0,1)
Matrix = matrix(Matrix,5,5)

# define R-vine pair-copula family matrix
family = c(0,1,3,4,4,0,0,3,4,1,0,0,0,4,1,0,0,0,0,3,0,0,0,0,0)
family = matrix(family,5,5)

# define R-vine pair-copula parameter matrix
par = c(0,0.2,0.9,1.5,3.9,0,0,1.1,1.6,0.9,0,0,0,1.9,0.5,
        0,0,0,0,4.8,0,0,0,0,0)
par = matrix(par,5,5)

# define second R-vine pair-copula parameter matrix
par2 = matrix(0,5,5)

# define RVineMatrix object
RVM = RVineMatrix(Matrix=Matrix,family=family,par=par,par2=par2,
                  names=c("V1","V2","V3","V4","V5"))

# simulate a sample of size 300 from the R-vine copula model
simdata = RVineSim(300,RVM)

# compute the Hessian matrix of the first row of the data
out2 = RVineHessian(simdata[1,],RVM)
out2$hessian