Last chance! 50% off unlimited learning
Sale ends in
Specifies an univariate GARCH time series model.
garchSpec(model = list(), presample = NULL,
cond.dist = c("norm", "ged", "std", "snorm", "sged", "sstd"),
rseed = NULL)
an object of class "fGARCHSPEC"
.
a character string naming the desired conditional distribution.
Valid values are "norm"
, "ged"
, "std"
,
"snorm"
, "sged"
, "sstd"
. The default value
is "norm"
, the standard normal distribution.
a list of GARCH model parameters, see section ‘Details’.
The default model=list()
specifies Bollerslev's
GARCH(1,1) model with normal conditional distributed innovations.
a numeric three column matrix with start values for the series, for the innovations, and for the conditional variances. For an ARMA(m,n)-GARCH(p,q) process the number of rows must be at least max(m,n,p,q)+1, longer presamples are truncated. Note, all presamples are initialized by a normal-GARCH(p,q) process.
single integer argument, the seed for the intitialization of
the random number generator for the innovations. If
rseed=NULL
, the default, then the state of the random
number generator is not touched by this function.
Diethelm Wuertz for the Rmetrics R-port.
The function garchSpec
specifies a GARCH or APARCH time
series process which we can use for simulating artificial GARCH
and/or APARCH models. This is very useful for testing the
GARCH parameter estimation results, since your model parameters
are known and well specified.
Argument model
is a list of model parameters. For the GARCH
part of the model they are:
omega
the constant coefficient of the variance equation,
by default 1e-6
;
alpha
the value or vector of autoregressive coefficients, by default 0.1, specifying a model of order 1;
beta
the value or vector of variance coefficients, by default 0.8, specifying a model of order 1.
If the model is APARCH, then the following additional parameters are available:
a positive number, the power of sigma in the volatility equation, it is 2 for GARCH models;
the leverage parameters, a vector of length
alpha
, containing numbers in the interval
The values for the linear part (conditional mean) are:
mu
the mean value, by default NULL;
ar
the autoregressive ARMA coefficients, by default NULL;
ma
the moving average ARMA coefficients, by default NULL.
The parameters for the conditional distributions are:
skew
the skewness parameter (also named "xi"), by default
0.9, effective only for the "dsnorm"
, the "dsged"
,
and the "dsstd"
skewed conditional distributions;
shape
the shape parameter (also named "nu"), by default 2
for the "dged"
and "dsged"
, and by default 4
for the "dstd"
and "dsstd"
conditional
distributions.
For example, specifying a subset AR(5[1,5])-GARCH(2,1) model with a standardized Student-t distribution with four degrees of freedom will return the following printed output:
garchSpec(model = list(ar = c(0.5,0,0,0,0.1), alpha =
c(0.1, 0.1), beta = 0.75, shape = 4), cond.dist = "std")
Formula:
~ ar(5) + garch(2, 1)
Model:
ar: 0.5 0 0 0 0.1
omega: 1e-06
alpha: 0.1 0.1
beta: 0.75
Distribution:
std
Distributional Parameter:
nu = 4
Presample:
time z h y
0 0 -0.3262334 2e-05 0
-1 -1 1.3297993 2e-05 0
-2 -2 1.2724293 2e-05 0
-3 -3 0.4146414 2e-05 0
-4 -4 -1.5399500 2e-05 0
"Formula" describes the formula expression specifying the generating process, "Model" lists the associated model parameters, "Distribution" the type of the conditional distribution function in use, "Distributional Parameters" lists the distributional parameter (if any), and the "Presample" shows the presample input matrix.
If we have specified presample=NULL
in the argument list,
then the presample is generated automatically by default as
norm-AR()-GARCH() process.
## garchSpec -
# Normal Conditional Distribution:
spec = garchSpec()
spec
# Skewed Normal Conditional Distribution:
spec = garchSpec(model = list(skew = 0.8), cond.dist = "snorm")
spec
# Skewed GED Conditional Distribution:
spec = garchSpec(model = list(skew = 0.9, shape = 4.8), cond.dist = "sged")
spec
## More specifications ...
# Default GARCH(1,1) - uses default parameter settings
garchSpec(model = list())
# ARCH(2) - use default omega and specify alpha, set beta=0!
garchSpec(model = list(alpha = c(0.2, 0.4), beta = 0))
# AR(1)-ARCH(2) - use default mu, omega
garchSpec(model = list(ar = 0.5, alpha = c(0.3, 0.4), beta = 0))
# AR([1,5])-GARCH(1,1) - use default garch values and subset ar[.]
garchSpec(model = list(mu = 0.001, ar = c(0.5,0,0,0,0.1)))
# ARMA(1,2)-GARCH(1,1) - use default garch values
garchSpec(model = list(ar = 0.5, ma = c(0.3, -0.3)))
# GARCH(1,1) - use default omega and specify alpha/beta
garchSpec(model = list(alpha = 0.2, beta = 0.7))
# GARCH(1,1) - specify omega/alpha/beta
garchSpec(model = list(omega = 1e-6, alpha = 0.1, beta = 0.8))
# GARCH(1,2) - use default omega and specify alpha[1]/beta[2]
garchSpec(model = list(alpha = 0.1, beta = c(0.4, 0.4)))
# GARCH(2,1) - use default omega and specify alpha[2]/beta[1]
garchSpec(model = list(alpha = c(0.12, 0.04), beta = 0.08))
# snorm-ARCH(1) - use defaults with skew Normal
garchSpec(model = list(beta = 0, skew = 0.8), cond.dist = "snorm")
# sged-GARCH(1,1) - using defaults with skew GED
garchSpec(model = list(skew = 0.93, shape = 3), cond.dist = "sged")
# Taylor Schwert GARCH(1,1) - this belongs to the family of APARCH Models
garchSpec(model = list(delta = 1))
# AR(1)-t-APARCH(2, 1) - a little bit more complex specification ...
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")
Run the code above in your browser using DataLab