VineCopula (version 1.3)

RVineSeqEst: Sequential estimation of an R-vine copula model

Description

This function sequentially estimates the pair-copula parameters of a d-dimensional R-vine copula model as specified by the corresponding RVineMatrix object.

Usage

RVineSeqEst(data, RVM, method="mle", se=FALSE, max.df=30,
            max.BB=list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1)), 
            progress=FALSE,weights=NA)

Arguments

data

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

RVM

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

method

Character indicating the estimation method: either pairwise maximum likelihood estimation (method = "mle"; default) or inversion of Kendall's tau (method = "itau"; see BiCopEst

se

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

max.df

Numeric; upper bound for the estimation of the degrees of freedom parameter of the t-copula (default: max.df = 30; for more details see BiCopEst).

max.BB

List; upper bounds for the estimation of the two parameters (in absolute values) of the BB1, BB6, BB7 and BB8 copulas (default: max.BB = list(BB1=c(5,6),BB6=c(6,6),BB7=c(5,6),BB8=c(6,1))).

progress

Logical; whether the pairwise estimation progress is printed (default: progress = FALSE).

weights

Numerical; weights for each observation (opitional).

Value

• RVM
  RVineMatrix object with the sequentially estimated parameters stored in RVM$par and RVM$par2.
• se
  Lower triangular d x d matrix with estimated standard errors of the (first) pair-copula parameters for each (conditional) pair defined in the RVineMatrix object (if se = TRUE).
• se2
  Lower triangular d x d matrix with estimated standard errors of the second parameters for pair-copula families with two parameters for each (conditional) pair defined in the RVineMatrix object (if se = TRUE).

Details

The pair-copula parameter estimation is performed tree-wise, i.e., for each R-vine tree the results from the previous tree(s) are used to calculate the new copula parameters using BiCopEst.

See Also

BiCopEst, BiCopHfunc, RVineLogLik, RVineMLE, RVineMatrix

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)

# sequential estimation
RVineSeqEst(simdata,RVM,method="itau",se=TRUE)
RVineSeqEst(simdata,RVM,method="mle",se=TRUE)