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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: SIMULATION:
# garchSim Simulates a GARCH/APARCH process
# .garchSim Simulates a GARCH/APARCH from specification object
################################################################################
garchSim =
function (model = list(omega = 1.0e-6, alpha = 0.1, beta = 0.8), n = 100,
n.start = 100, presample = NULL, cond.dist = c("rnorm", "rged", "rstd",
"rsnorm", "rsged", "rsstd"), rseed = NULL)
{ # A function implemented by Diethelm Wuertz
# Description:
# Simulates a time series process from the GARCH family
# Arguments:
# model - either a specification object of class 'garchSpec'
# or a list with the model parameters as entries
# ar - a vector of autoregressive coefficients of
# length m for the ARMA specification,
# ma - a vector of moving average coefficients of
# length n for the ARMA specification,
# omega - the variance value for GARCH/APARCH
# specification,
# alpha - a vector of autoregressive coefficients
# of length p for the GARCH/APARCH specification,
# gamma - a vector of leverage coefficients of
# length p for the APARCH specification,
# beta - a vector of moving average coefficients of
# length q for the GARCH/APARCH specification,
# mu - the mean value for ARMA specification,
# delta - the exponent value used in the variance
# equation.
# skew - a numeric value for the skew parameter.
# shape - a numeric value for the shape parameter.
# n - an integer, the length of the series
# n.start - the length of the warm-up sequence to reduce the
# effect of initial conditions.
# presample - either a multivariate "timeSeries", a
# multivariate "ts", a "data.frame" object or a numeric
# "matrix" with 3 columns and at least max(m,n,p,q)
# rows. The first culumn ...
# cond.dist - a character string naming the conditional distribution
# function. Valid strings are: "rnorm", "rged", "rstd", "rsnorm",
# "rsged", and "rsstd".
# Notes:
# The parameters omega, alpha, and beta in the model list
# must be explicitely specified, otherwise a warning message
# will be printed. The other parameters will be assigned by
# default values.
# FUNCTION:
# Simulate Series:
if (class(model) == "list") {
# Create Specification Object:
spec = garchSpec(model = model, presample = presample,
cond.dist = cond.dist, rseed = rseed)
ans = .garchSim(n = n, n.start = n.start, spec = spec)
} else if (class(model) == "garchSpec") {
ans = .garchSim(n = n, n.start = n.start, spec = model)
} else {
stop("model must be an object of class list or garchSpec")
}
# Return Value:
ans
}
# ------------------------------------------------------------------------------
.garchSim =
function(n = 1000, n.start = 1000, spec = garchSpec())
{ # A function implemented by Diethelm Wuertz
# Description:
# Simulates GARCH series from 'garchSpec'
# Arguments:
# n - length of time series
# spec - GARCH specification structure
# FUNCTION:
# Random Seed:
if (spec@rseed != 0) set.seed(spec@rseed)
# Enlarge Series:
n = n + n.start
# Determine Orders:
order.ar = order.ma = order.alpha = order.gamma = order.beta = 1
if (sum(abs(spec@model$ar)) != 0) {
model.ar = spec@model$ar
order.ar = length(spec@model$ar)
} else {
model.ar = 0
}
if (sum(abs(spec@model$ma)) != 0) {
model.ma = spec@model$ma
order.ma = length(spec@model$ma)
} else {
model.ma = 0
}
if (sum(abs(spec@model$alpha)) != 0) {
model.alpha = spec@model$alpha
order.alpha = length(spec@model$alpha)
} else {
model.alpha = 0
}
if (sum(abs(spec@model$gamma)) != 0) {
model.gamma = spec@model$gamma
order.gamma = length(spec@model$gamma)
} else {
model.gamma = 0
}
if (sum(abs(spec@model$beta)) != 0) {
model.beta = spec@model$beta
order.beta = length(spec@model$beta)
} else {
model.beta = 0
}
# Create Innovations:
if (spec@distribution == "rnorm")
z = rnorm(n)
if (spec@distribution == "rged")
z = rged(n, nu = spec@model$shape)
if (spec@distribution == "rstd")
z = rstd(n, nu = spec@model$shape)
if (spec@distribution == "rsnorm")
z = rsnorm(n, xi = spec@model$skew)
if (spec@distribution == "rsged")
z = rsged(n, nu = spec@model$shape, xi = spec@model$skew)
if (spec@distribution == "rsstd")
z = rsstd(n, nu = spec@model$shape, xi = spec@model$skew)
# Expand to whole Sample:
delta = spec@model$delta
z = c(rev(spec@presample[, 1]), z)
h = c(rev(spec@presample[, 2])^delta, rep(NA, times = n))
y = c(rev(spec@presample[, 3]), rep(NA, times = n))
m = length(spec@presample[, 1])
names(z) = names(h) = names(y) = NULL
# Iterate APARCH Model:
# [This includes the GARCH case]
deltainv = 1/delta
eps = h^deltainv*z
for (i in (m+1):(n+m)) {
h[i] = spec@model$omega +
sum(model.alpha*(abs(eps[i-(1:order.alpha)]) -
model.gamma*(eps[i-(1:order.alpha)]))^delta) +
sum(model.beta*h[i-(1:order.beta)])
eps[i] = h[i]^deltainv * z[i]
y[i] = spec@model$mu +
sum(model.ar*y[i-(1:order.ar)]) +
sum(model.ma*(h[i-(1:order.ma)]**deltainv)) + eps[i]
}
# Sample:
data = cbind(
z = z[(m+1):(n+m)],
h = h[(m+1):(n+m)]^deltainv,
y = y[(m+1):(n+m)])
rownames(data) = as.character(1:n)
data = data[-(1:n.start),]
# Add Series:
# spec@series = data[, 1:2]
ans = ts(as.vector(data[, 3]))
attr(ans, "spec") = spec
# Return Value:
ans
}
################################################################################
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