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\name{garchSim}
\alias{garchSim}
\title{Univariate GARCH/APARCH Time Series Simulation}
\description{
Simulates a univariate GARCH/APARCH time series model.
}
\usage{
garchSim(spec = garchSpec(), n = 100, n.start = 100, extended = FALSE)
}
\arguments{
\item{extended}{
logical parameter if the output series should be a 3 columns
\code{timeSeries} object with \code{garch}, \code{sigma} and
\code{eps} data (\code{extended = TRUE}) or a univariate GARCH\\APARCH time
series (\code{extended = FALSE}
}
\item{spec}{
a specification object of class \code{"fGARCHSPEC"} as
returned by the function \code{garchSpec}. The model parameters
are taken from the \code{@model} slot, a list with the
following entries:\cr
\code{omega} - the constant coefficient of the variance equation,
by default 1e-6; \cr
\code{alpha} - the value or vector of autoregressive coefficients,
by default 0.1, specifying a model of order 1; \cr
\code{beta} - the value or vector of variance coefficients,
by default 0.8, specifying a model of order 1;
\cr
The optional values for the linear part are: \cr
\code{mu} - the intercept value, by default 0 (it implies that the mean = mu/(1-sum(ar))); \cr
\code{ar} - the autoregressive ARMA coefficients, by default 0; \cr
\code{ma} - the moving average ARMA coefficients, by default 0.
\cr
The optional parameters for the conditional distributions are:\cr
\code{skew} - the skewness parameter (also named xi), by default
0.9, effective only for the \code{"dsnorm"}, the \code{"dsged"},
and the \code{"dsstd"} skewed conditional distributions; \cr
\code{shape} = the shape parameter (also named nu), by default 2
for the \code{"dged"} and \code{"dsged"}, and by default 4
for the \code{"dstd"} and \code{"dsstd"} conditional
distributions.\cr
See also below for further details.
}
\item{n}{
length of output series, an integer value. An integer value,
by default \code{n=100}.
}
\item{n.start}{
length of "burn-in" period, by default 100.
}
}
\details{
The function \code{garchSim} simulates an univariate GARCH or
APARCH time series process as specified by the argument \code{model}.
The \code{model} is an object of class \code{"fGARCHSPEC"} as
returned by the function \code{garchSpec}. The returned model
specification comes comes with a slot \code{@model} which is
a list of just the numeric parameter entries. These are recognized
and extracted for use by the function \code{garchSim}.
By default the series will be returned as an object of class
\code{"ts"} or as a \code{"numeric"} vector. Having time/date
positions, e.g. from an empirical process the numeric vector
can be easily transformed into other time series objects like
\code{"timeSeries"} or \code{"zoo"}. So one can estimate the
parameters of a GARCH process from empirical data using the
function \code{garchFit} and simulate than statistically
equivalent GARCH processes with the same set of model parameters
using the function \code{garchSim}.
The third entry in the argument \code{returnClass="mts"} allows
to return a trivariate time series, where the first column contains
the simulated \code{"garch"} process, the second column the conditional
standard deviations \code{"h"}, and the last column the innovations
named \code{"eps"}.
Note, the default model specifies Bollerslev's GARCH(1,1) model
with normal distributed innovations.
}
\value{
The function \code{garchSim} returns an objects of class
\code{"timeSeries"} attributed by a list with entry
\code{$garchSpec} giving the GARCH specification structure as
returned by the function \code{garchSpec} and with information on
conditional standard deviations and innovations. See details above.
}
\author{
Diethelm Wuertz for the Rmetrics \R-port.
}
\examples{
## garchSpec -
spec = garchSpec()
spec
## garchSim -
# Simulate a "timeSeries" object:
x = garchSim(spec, n = 50)
class(x)
print(x)
## More simulations ...
# Default GARCH(1,1) - uses default parameter settings
spec = garchSpec(model = list())
garchSim(spec, n = 10)
# ARCH(2) - use default omega and specify alpha, set beta=0!
spec = garchSpec(model = list(alpha = c(0.2, 0.4), beta = 0))
garchSim(spec, n = 10)
# AR(1)-ARCH(2) - use default mu, omega
spec = garchSpec(model = list(ar = 0.5, alpha = c(0.3, 0.4), beta = 0))
garchSim(spec, n = 10)
# AR([1,5])-GARCH(1,1) - use default garch values and subset ar[.]
spec = garchSpec(model = list(mu = 0.001, ar = c(0.5,0,0,0,0.1)))
garchSim(spec, n = 10)
# ARMA(1,2)-GARCH(1,1) - use default garch values
spec = garchSpec(model = list(ar = 0.5, ma = c(0.3, -0.3)))
garchSim(spec, n = 10)
# GARCH(1,1) - use default omega and specify alpha/beta
spec = garchSpec(model = list(alpha = 0.2, beta = 0.7))
garchSim(spec, n = 10)
# GARCH(1,1) - specify omega/alpha/beta
spec = garchSpec(model = list(omega = 1e-6, alpha = 0.1, beta = 0.8))
garchSim(spec, n = 10)
# GARCH(1,2) - use default omega and specify alpha[1]/beta[2]
spec = garchSpec(model = list(alpha = 0.1, beta = c(0.4, 0.4)))
garchSim(spec, n = 10)
# GARCH(2,1) - use default omega and specify alpha[2]/beta[1]
spec = garchSpec(model = list(alpha = c(0.12, 0.04), beta = 0.08))
garchSim(spec, n = 10)
# snorm-ARCH(1) - use defaults with skew Normal
spec = garchSpec(model = list(beta = 0, skew = 0.8), cond.dist = "snorm")
garchSim(spec, n = 10)
# sged-GARCH(1,1) - using defaults with skew GED
model = garchSpec(model = list(skew = 0.93, shape = 3), cond.dist = "sged")
garchSim(model, n = 10)
# Taylor Schwert GARCH(1,1) - this belongs to the family of APARCH Models
spec = garchSpec(model = list(delta = 1))
garchSim(spec, n = 10)
# AR(1)-t-APARCH(2, 1) - a little bit more complex specification ...
spec = garchSpec(model = list(mu = 1.0e-4, ar = 0.5, omega = 1.0e-6,
alpha = c(0.10, 0.05), gamma = c(0, 0), beta = 0.8, delta = 1.8,
shape = 4, skew = 0.85), cond.dist = "sstd")
garchSim(spec, n = 10)
}
\keyword{models}
|
