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# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA
# Copyrights (C)
# for this R-port:
# 1999 - 2007, Diethelm Wuertz, GPL
# Diethelm Wuertz <wuertz@itp.phys.ethz.ch>
# info@rmetrics.org
# www.rmetrics.org
# for the code accessed (or partly included) from other R-ports:
# see R's copyright and license files
# for the code accessed (or partly included) from contributed R-ports
# and other sources
# see Rmetrics's copyright file
################################################################################
# FUNCTION: ELLIPTICAL COPULAE PARAMETER FITTING:
# ellipticalCopulaSim Simulates bivariate elliptical copula
# ellipticalCopulaFit Fits the paramter of an elliptical copula
################################################################################
################################################################################
# FUNCTION: ELLIPTICAL COPULAE PARAMETER FITTING:
# ellipticalCopulaSim Simulates bivariate elliptical copula
# ellipticalCopulaFit Fits the paramter of an elliptical copula
ellipticalCopulaSim =
function (n, rho = 0.75, param = NULL, type = c("norm", "cauchy", "t"))
{ # A function implemented by Diethelm Wuertz
# Description:
# Simulates bivariate elliptical Copula
# Match Arguments:
type = match.arg(type)
# "norm" Random Deviates:
if (type == "norm") {
ans = .rnormCopula(n = n, rho = rho)
}
# "cauchy" Random Deviates:
if (type == "cauchy") {
ans = .rcauchyCopula(n = n, rho = rho)
}
# "t" Random Deviates:
if (type == "t") {
if (is.null(param)) {
param = c(nu = 4)
} else {
param = c(nu = param[1])
}
ans = .rtCopula(n = n, rho = rho, nu = param)
}
# "logistic" Random Deviates:
# NOT YET IMPLEMENTED ...
# "laplace" Random Deviates:
# NOT YET IMPLEMENTED ...
# "kotz" Random Deviates:
# NOT YET IMPLEMENTED ...
# "epower" Random Deviates:
# NOT YET IMPLEMENTED ...
# Control:
control = list(rho = rho, param = param, type = type)
attr(ans, "control") = unlist(control)
# Return Value:
ans
}
# ------------------------------------------------------------------------------
ellipticalCopulaFit =
function(u, v = NULL, type = c("norm", "cauchy", "t"), ...)
{ # A function implemented by Diethelm Wuertz
# Description:
# Fits the paramter of an elliptical copula
# Note:
# The upper limit for nu is 100
# FUNCTION:
# Match Arguments:
type = match.arg(type)
# Settings:
U = u
V = v
if (is.list(u)) {
u = u[[1]]
v = u[[2]]
}
if (is.matrix(u)) {
U = u[, 1]
V = u[, 2]
}
U <<- u
V <<- v
# Estimate Rho from Kendall's tau for all types of Copula:
tau = cor(x = U, y = V, method = "kendall") #[1, 2]
Rho = rho = sin((pi*tau/2))
# Estimate "norm" Copula:
if (type == "norm") {
fun = function(x) {
-mean( log(.dnormCopula(u = U, v = V, rho = x)) )
}
fit = nlminb(start = rho, objective = fun, lower = -1, upper = 1, ...)
}
# Estimate "cauchy" Copula:
if (type == "cauchy") {
fun = function(x) {
-mean( log(.dcauchyCopula(u = U, v = V, rho = x)) )
}
fit = nlminb(start = rho, objective = fun, lower = -1, upper = 1, ...)
}
# Estimate "t" Copula:
if (type == "t") {
fun = function(x) {
-mean( log(.dtCopula(u = U, v = V, rho = x[1], nu = x[2])) )
}
fit = nlminb(start = c(rho = rho, nu = 4), objective = fun,
lower = c(-1, 1), upper = c(1, Inf), ...)
fit$Nu = 4
}
# Estimate "logistic" Copula:
if (type == "logistic") {
# NOT YET IMPLEMENTED ...
fun = function(x) {
-mean( log(dellipticalCopula(u = U, v = V, ...)) )
}
fit = nlminb(start = c(), objective = fun,
lower = c(rho = -1, NA), upper = c(rho = 1, NA), ...)
}
# Estimate "laplace" Copula:
if (type == "laplace") {
# NOT YET IMPLEMENTED ...
fun = function(x) {
-mean( log(dellipticalCopula(u = U, v = V, ...)) )
}
fit = nlminb(start = c(), objective = fun,
lower = c(rho = -1, NA), upper = c(rho = 1, NA), ...)
}
# Estimate "kotz" Copula:
if (type == "kotz") {
# NOT YET IMPLEMENTED ...
fun = function(x) {
-mean( log(dellipticalCopula(u = U, v = V, ...)) )
}
fit = nlminb(start = c(), objective = fun,
lower = c(rho = -1, NA), upper = c(rho = 1, NA), ...)
}
# Estimate "epower" Copula:
if (type == "epower") {
# NOT YET IMPLEMENTED ...
fun = function(x) {
-mean( log(dellipticalCopula(u = U, v = V, ...)) )
}
fit = nlminb(start = c(), objective = fun,
lower = c(rho = -1, NA), upper = c(rho = 1, NA), ...)
}
# Keep Start Value:
# fit$Rho = Rho
# Return Value:
fit
}
################################################################################
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