RVineStdError {VineCopula}

Standard Errors of an R-Vine Copula Model

Description

This function calculates the standard errors of a d-dimensional R-vine copula model given the Hessian matrix.

Usage

RVineStdError(hessian, RVM)

Arguments

hessian

The Hessian matrix of the given R-vine.

RVM

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

Value

se

The calculated standard errors for the first parameter matrix. The entries are ordered with respect to the ordering of the RVM$par matrix.

se2

The calculated standard errors for the second parameter matrix.

Note

The negative Hessian matrix should be positive semidefinite. Otherwise NAs will be returned in some entries and the non-NA entries may be wrong. If the negative Hessian matrix is negative definite, then one could try a near positive matrix. The package Matrix provides a function called nearPD to estimate a matrix which is positive definite and close to the given matrix.

Author(s)

Ulf Schepsmeier, Jakob Stoeber

References

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#.

See Also

BiCopDeriv(), BiCopDeriv2(), BiCopHfuncDeriv(), BiCopHfuncDeriv2(),
RVineMatrix(), RVineHessian(), 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
set.seed(123)
simdata <- RVineSim(300, RVM)

# compute the Hessian matrix of the first row of the data
out2 <- RVineHessian(simdata,RVM)

# get the standard errors
RVineStdError(out2$hessian, RVM)