Hessian Matrix of the Log-Likelihood of an R-Vine Copula Model
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.
RVineHessian(data, RVM)
data |
An N x d data matrix (with uniform margins). |
RVM |
An |
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. |
The Hessian matrix is not available for R-vine copula models with two parameter Archimedean copulas, i.e. BB1, BB6, BB7, BB8 and their rotated versions.
Ulf Schepsmeier, Jakob Stoeber
Dissmann, J. F., E. C. Brechmann, C. Czado, and D. Kurowicka (2013). Selecting and estimating regular vine copulae and application to financial returns. Computational Statistics & Data Analysis, 59 (1), 52-69.
Schepsmeier, U. and J. Stoeber (2014) Derivatives and Fisher information of bivariate copulas. Statistical Papers, 55(2), 525-542. online first: https://link.springer.com/article/10.1007/s00362-013-0498-x.
Web supplement: Derivatives and Fisher Information of bivariate copulas. https://mediatum.ub.tum.de/node?id=1119201
Stoeber, J. and U. Schepsmeier (2013). Estimating standard errors in regular vine copula models. Computational Statistics, 28 (6), 2679-2707 https://link.springer.com/article/10.1007/s00180-013-0423-8#.
# 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
set.seed(123)
simdata <- RVineSim(300, RVM)
# compute the Hessian matrix of the first row of the data
out2 <- RVineHessian(simdata[1,], RVM)
out2$hessianPlease choose more modern alternatives, such as Google Chrome or Mozilla Firefox.