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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: DESCRIPTION:
# garchKappa Computes Expection for APARCH Models
# .garchKappaFun Internal function used by garchKappa()
# FUNCTION: DESCRIPTION:
# .truePersistence Computes true persistence
################################################################################
garchKappa <-
function(cond.dist = c("norm", "ged", "std", "snorm", "sged", "sstd",
"snig"), gamma = 0, delta = 2, skew = NA, shape = NA)
{
# A function implemented by Diethelm Wuertz
# Description:
# Computes Expection for APARCH Models
# FUNCTION:
# Compute kappa:
kappa = integrate(.garchKappaFun, lower = -Inf, upper = Inf, cond.dist =
cond.dist[1], gamma = gamma, delta = delta, skew = skew, shape =
shape)[[1]]
names(kappa) = "kappa"
attr(kappa, "control") =
c(gamma = gamma, delta = delta, skew = skew, shape = shape)
attr(kappa, "cond.dist") = cond.dist[1]
# Return Value:
kappa
}
# ------------------------------------------------------------------------------
.garchKappaFun <-
function(x,
cond.dist = c("norm", "ged", "std", "snorm", "sged", "sstd", "snig"),
gamma = 0, delta = 2, skew = NA, shape = NA)
{
# A function implemented by Diethelm Wuertz
# Description:
# Internal function used by kappa()
# FUNCTION:
# Compute Expectation Value for ...
funcE = (abs(x) - gamma*x)^delta
# Select Appropriate Conditional Density:
cond.dist = cond.dist[1]
if (cond.dist == "norm") {
fun = funcE * dnorm(x)
}
if (cond.dist == "ged") {
fun = funcE * dged(x, nu = shape)
}
if (cond.dist == "std") {
fun = funcE * dstd(x, nu = shape)
}
if (cond.dist == "snorm") {
fun = funcE * dsnorm(x, xi = skew)
}
if (cond.dist == "sged") {
fun = funcE * dsged(x, nu = shape, xi = skew)
}
if (cond.dist == "sstd") {
fun = funcE * dsstd(x, nu = shape, xi = skew)
}
if (cond.dist == "snig") {
fun = funcE * dsnig(x, zeta = shape, rho = skew)
}
# Return Value:
fun
}
################################################################################
.truePersistence <-
function(fun = "norm", alpha = 1, gamma = 0, beta = 0, delta = 1, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Computes persistence for an APARCH process
# Arguments:
# fun - name of density functions of APARCH innovations
# alpha, gamma - numeric value or vector of APARCH coefficients,
# must be of same length
# beta - numeric value or vector of APARCH coefficients
# delta - numeric value of APARCH exponent
# Note:
# fun is one of: norm, snorn, std, sstd, ged, sged, snig
# FUNCTION:
# Match Density Function:
fun = match.fun(fun)
# Persisgtence Function: E(|z|-gamma z)^delta
e = function(x, gamma, delta, ...) {
(abs(x)-gamma*x)^delta * fun(x, ...)
}
# Compute Persistence by Integration:
persistence = sum(beta)
for (i in 1:length(alpha)) {
I = integrate(e, -Inf, Inf, subdivisions = 1000,
rel.tol = .Machine$double.eps^0.5,
gamma = gamma[i], delta = delta, ...)
persistence = persistence + alpha[i] * I[[1]]
}
# Warning:
if (persistence >= 1) {
p = as.character(round(persistence, digits = 3))
warning(paste("Divergent persistence p =", p))
}
# Return Value:
persistence
}
################################################################################
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