copula (version 0.999-19)

ellipCopula: Construction of Elliptical Copula Class Objects

Description

Constructs an elliptical copula class object with its corresponding parameters and dimension.

Usage

ellipCopula (family, param, dim = 2, dispstr = "ex", df = 4, ...)
normalCopula(param, dim = 2, dispstr = "ex")
     tCopula(param, dim = 2, dispstr = "ex", df = 4, df.fixed = FALSE, df.min = 0.01)

Arguments

family

a character string specifying the family of an elliptical copula. Must be "normal" (the default) or "t".

param

a numeric vector specifying the parameter values; P2p() accesses this vector, whereas p2P() and getSigma() provide the corresponding “P” matrix, see below.

dim

the dimension of the copula.

dispstr

a character string specifying the type of the symmetric positive definite matrix characterizing the elliptical copula. Currently available structures are "ex" for exchangeable, "ar1" for \(AR(1)\), "toep" for Toeplitz (toeplitz), and "un" for unstructured.

df

integer value specifying the number of degrees of freedom of the multivariate t distribution used to construct the t copulas.

df.fixed

logical specifying if the degrees of freedom df will be considered as a parameter (to be estimated) or not. The default, FALSE, means that df is to be estimated if the object is passed as argument to fitCopula.

df.min

non-negative number; the strict lower bound for df, mainly during fitting when df.fixed=FALSE, with fitCopula.

…

currently nothing.

Value

An elliptical copula object of class "'>normalCopula" or "'>tCopula".

See Also

p2P(), and getSigma() for construction and extraction of the dispersion matrix \(P\) or \(Sigma\) matrix of (generalized) correlations.

archmCopula, fitCopula.

Examples

# NOT RUN {
norm.cop <- normalCopula(c(0.5, 0.6, 0.7), dim = 3, dispstr = "un")
t.cop <- tCopula(c(0.5, 0.3), dim = 3, dispstr = "toep",
                 df = 2, df.fixed = TRUE)
getSigma(t.cop) # P matrix (with diagonal = 1)

## dispersion "AR1" :
nC.7 <- normalCopula(0.8, dim = 7, dispstr = "ar1")
getSigma(nC.7) ##-> toeplitz( (1  0.8  0.8^2  0.8^3  ... 0.8^6) ) matrix

## from the wrapper
norm.cop <- ellipCopula("normal", param = c(0.5, 0.6, 0.7),
                        dim = 3, dispstr = "un")
if(require("scatterplot3d") && dev.interactive(orNone=TRUE)) {
  ## 3d scatter plot of 1000 random observations
  scatterplot3d(rCopula(1000, norm.cop))
  scatterplot3d(rCopula(1000, t.cop))
}
set.seed(12)
uN <- rCopula(512, norm.cop)
set.seed(2); pN1 <- pCopula(uN, norm.cop)
set.seed(3); pN2 <- pCopula(uN, norm.cop)
stopifnot(all.equal(pN1, pN2, 1e-4))# see 5.711e-5
(Xtras <- copula:::doExtras())
if(Xtras) { ## a bit more accurately:
  set.seed(4); pN1. <- pCopula(uN, norm.cop, abseps = 1e-9)
  set.seed(5); pN2. <- pCopula(uN, norm.cop, abseps = 1e-9)
  stopifnot(all.equal(pN1., pN2., 1e-5))# see 3.397e-6
  ## but increasing the required precision (e.g., abseps=1e-15) does *NOT* help
}

## For smaller copula dimension 'd', alternatives are available and
## non-random, see ?GenzBretz from package 'mvtnorm' :
require("mvtnorm")# -> GenzBretz(), Miva(), and TVPACK() are available
## Note that Miwa() would become very slow for dimensions 5, 6, ..
set.seed(4); pN1.M <- pCopula(uN, norm.cop, algorithm = Miwa(steps = 512))
set.seed(5); pN2.M <- pCopula(uN, norm.cop, algorithm = Miwa(steps = 512))
stopifnot(all.equal(pN1.M, pN2.M, tol= 1e-15))# *no* randomness
set.seed(4); pN1.T <- pCopula(uN, norm.cop, algorithm = TVPACK(abseps = 1e-10))
set.seed(5); pN2.T <- pCopula(uN, norm.cop, algorithm = TVPACK(abseps = 1e-14))
stopifnot(all.equal(pN1.T, pN2.T, tol= 1e-15))# *no* randomness (but no effect of 'abseps')


## Versions with unspecified parameters:
tCopula()
allEQ <- function(u,v) all.equal(u, v, tolerance=0)
stopifnot(allEQ(ellipCopula("norm"), normalCopula()),
          allEQ(ellipCopula("t"), tCopula()))
tCopula(dim=3)
tCopula(dim=4, df.fixed=TRUE)
tCopula(dim=5, disp = "toep", df.fixed=TRUE)
normalCopula(dim=4, disp = "un")
# }

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