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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
################################################################################
# FUNCTION: PARAMETER ESTIMATION:
# .gogarchFit Fits the parameters of a GO-GARCH process
################################################################################
.gogarchFit <-
function(formula = ~ garch(1, 1), data,
init.rec = c("mci", "uev"),
delta = 2,
skew = 1,
shape = 4,
cond.dist = c("norm", "snorm", "ged", "sged", "std", "sstd", "snig", "QMLE"),
include.mean = TRUE,
include.delta = NULL,
include.skew = NULL,
include.shape = NULL,
leverage = NULL,
trace = TRUE,
algorithm = c("nlminb", "lbfgsb", "nlminb+nm", "lbfgsb+nm"),
hessian = c("ropt", "rcd"),
control = list(),
title = NULL,
description = NULL,
...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Fits a GO-Garch Model using Independent Component Analysis
# Arguments:
# The arguments are the same as for the univariate case.
# formula - formula for all marginal models
# data - multivariate timeSeries object
# ...
# Value:
# S4 Object of class (univariate) fGARCH ...
# Notes:
# This function has still a preliminary status ...
# This function was inspired from the contributed gogarch
# package of Bernhard Pfaff.
# Example:
# require(fEcofin); data(DowJones30)
# X = returns(as.timeSeries(DowJones30)); head(X)
# N = 5; ans = .gogarchFit(data = X[, 1:N], trace = FALSE); ans
# ans@h.t
# FUNCTION:
# Multivariate ?
stopifnot(isMultivariate(data))
# Data:
X = data
# Marginal Garch Models:
garchControl = list(
init.rec = init.rec, delta = delta, skew = skew, shape = shape,
cond.dist = cond.dist, include.mean = include.mean,
include.delta = include.delta, include.skew = include.skew,
include.shape = include.shape, leverage = leverage,
trace = trace, algorithm = algorithm, hessian = hessian,
control = control, title = title, description = description)
# Compute fastICA:
# ... the following lines of code were borrowed from
# Bernhard Pfaff's contributed package gogarch
V <- t(X) %*% X / nrow(X)
svd <- svd(V)
P <- svd$u
Dsqr <- diag(sqrt(svd$d))
# set.seed(4711)
ica <- fastICA::fastICA(X, n.comp = ncol(X))
Z <- P %*% Dsqr %*% t(P) %*% ica$W
colnames(Z) = rownames(Z) = colnames(data)
Y <- X %*% solve(Z)
# Fit Marginal Garch Models:
fit <- apply(Y, 2, function(x) do.call("garchFit",
c(list(formula = formula, data = x), garchControl)))
# Compute Conditional Variances:
# ... the following lines of code were borrowed from
# Bernhard Pfaff's contributed package gogarch
H <- matrix(unlist(lapply(fit, function(x) x@h.t)),
ncol = ncol(X), nrow = nrow(X))
Hdf <- data.frame(t(H))
rownames(Hdf) <- colnames(data)
colnames(Hdf) <- rownames(data)
H.t <- lapply(Hdf, function(x) Z %*% diag(x) %*% t(Z))
# Add Title and Description:
if(is.null(title)) title = "ICA GO-GARCH Modelling"
if(is.null(description)) description = description()
# Result:
ans <- new("fGARCH",
call = as.call(match.call()),
formula = formula,
method = "ICA go-Garch Parmeter Estimation",
data = c(Records = nrow(data), Instruments = ncol(data)),
fit = fit,
residuals = numeric(),
fitted = numeric(),
h.t = c(Records = length(H.t), Dimension =dim(H.t[[1]])),
sigma.t = numeric(),
title = title,
description = description
)
# Multivariate Series:
attr(ans@data, "data") <- data
attr(ans@h.t, "H.t") <- H.t
# Return Value:
ans
}
################################################################################
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