VineCopula: RVineSeqEst – R documentation

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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,
  cores = 1
)

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`	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].
`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 (optional).
`cores`	integer; if `cores > 1`, estimation will be parallelized within each tree (using `foreach::foreach()`). However, the overhead caused by parallelization is likely to make the function run slower unless sample size is really large and `method = "itau"`.

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().

Value

An RVineMatrix() object with the sequentially estimated parameters stored in RVM$par and RVM$par2. The object is augmented by 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,
`nobs`	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),
`emptau`	matrix of empirical values of Kendall's tau,
`p.value.indeptest`	matrix of p-values of the independence test.

Note

For a comprehensive summary of the fitted model, use summary(object); to see all its contents, use str(object).

Author(s)

Ulf Schepsmeier, Jeffrey Dissmann, Thomas Nagler

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)

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

VineCopula

Statistical Inference of Vine Copulas

v2.4.1

GPL (>= 2)

Authors

Thomas Nagler [aut, cre], Ulf Schepsmeier [aut], Jakob Stoeber [aut], Eike Christian Brechmann [aut], Benedikt Graeler [aut], Tobias Erhardt [aut], Carlos Almeida [ctb], Aleksey Min [ctb, ths], Claudia Czado [ctb, ths], Mathias Hofmann [ctb], Matthias Killiches [ctb], Harry Joe [ctb], Thibault Vatter [ctb]

Initial release