| GarchFitting {fGarch} | R Documentation |
Estimates the parameters of an univariate GARCH process.
garchFit(formula, data, init.rec = c("mci", "uev"), delta = 2, skew = 1,
shape = 4, cond.dist = c("dnorm", "dsnorm", "dged", "dsged", "dstd", "dsstd"),
include.mean = TRUE, include.delta = NULL, include.skew = NULL,
include.shape = NULL, leverage = NULL, trace = TRUE,
algorithm = c("nlminb", "sqp", "lbfgsb", "nlminb+nm", "lbfgsb+nm"),
control = list(), title = NULL, description = NULL, ...)
garchKappa(cond.dist = c("dnorm", "dged", "dstd", "dsnorm", "dsged", "dsstd"),
gamma = 0, delta = 2, skew = NA, shape = NA)
algorithm |
a string parameter that determines the algorithm used for maximum
likelihood estimation. Allowed values are "sqp",
"nlminb", and "bfgs" where the first is the default
setting.
|
cond.dist |
a character string naming the desired conditional distribution.
Valid values are "dnorm", "dged", "dstd",
"dsnorm", "dsged", "dsstd". The default value
is the normal distribution.
|
control |
control parameters, the same as used for the functions from
nlminb, and 'bfgs' and 'Nelder-Mead' from optim.
|
data |
an optional timeSeries or data frame object containing the variables
in the model. If not found in data, the variables are taken
from environment(formula), typically the environment from which
armaFit is called. If data is an univariate series, then
the series is converted into a numeric vector and the name of the
response in the formula will be neglected.
|
delta, include.delta |
the exponent delta of the variance recursion. By default,
this value will be fixed, otherwise the exponent will be estimated
together with the other model parameters if include.delta=FALSE.
|
description |
a character string which allows for a brief description. |
formula |
formula object describing the mean and variance equation of the
ARMA-GARCH/APARCH model. A pure GARCH(1,1) model is selected
when e.g. formula=~garch(1,1). To specify for example an
ARMA(2,1)-APARCH(1,1) use formula = ~arma(2,1)+apaarch(1,1).
|
gamma |
APARCH leverage parameter entering into the formula for calculating the expectation value. |
include.mean |
this flag determines if the parameter for the mean will be estimated
or not. If include.mean=TRUE this will be the case, otherwise
the parameter will be kept fixed durcing the process
of parameter optimization.
|
include.skew, include.shape |
this flag determines if the parameters for the skew and shape
of the conditional distribution will be estimated or not. If
include.skew=TRUE and/or include.shape=TRUE this will
be the case, otherwise the parameters will be kept fixed durcing
the process of parameter optimization.
|
init.rec |
a character string indicating the method how to initialize the mean and varaince recursion relation. |
leverage |
a logical flag for APARCH models. Should the model be leveraged?
By default leverage=TRUE.
|
skew, shape |
skewness and shape parameter of the conditional distribution. |
title |
a character string which allows for a project title. |
trace |
a logical flag. Should the optimization process of fitting the
model parameters be printed? By default trace=TRUE.
|
... |
additional arguments to be passed. |
garchFit
returns a S4 object of class fGARCH with the following slots:
@call |
the call of the garch function.
|
@formula |
a list with two formula entries, one for the mean and the other one for the variance equation. |
@method |
a string denoting the optimization method, by default the returneds string is "Max Log-Likelihood Estimation". |
@data |
a list with one entry named x, containing the data of
the time series to be estimated, the same as given by the
input argument series.
|
@fit |
a list with the results from the parameter estimation. The entries of the list depend on the selected algorithm, see below. |
@residuals |
a numeric vector with the residual values. |
@fitted |
a numeric vector with the fitted values. |
@h.t |
a numeric vector with the conditional variances. |
@sigma.t |
a numeric vector with the conditional variances. |
@title |
a title string. |
@description |
a string with a brief description. |
The entries of the @fit slot show the results from the
optimization.
Diethelm Wuertz for the Rmetrics R-port,
R Core Team for the 'optim' R-port,
Douglas Bates and Deepayan Sarkar for the 'nlminb' R-port,
Bell-Labs for the underlying PORT Library,
Ladislav Luksan for the underlying Fortran SQP Routine,
Zhu, Byrd, Lu-Chen and Nocedal for the underlying L-BFGS-B Routine.
ATT (1984); PORT Library Documentation, http://netlib.bell-labs.com/netlib/port/.
Bera A.K., Higgins M.L. (1993); ARCH Models: Properties, Estimation and Testing, J. Economic Surveys 7, 305–362.
Bollerslev T. (1986); Generalized Autoregressive Conditional Heteroscedasticity, Journal of Econometrics 31, 307–327.
Byrd R.H., Lu P., Nocedal J., Zhu C. (1995); A Limited Memory Algorithm for Bound Constrained Optimization, SIAM Journal of Scientific Computing 16, 1190–1208.
Engle R.F. (1982); Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica 50, 987–1008.
Nash J.C. (1990); Compact Numerical Methods for Computers, Linear Algebra and Function Minimisation, Adam Hilger.
Nelder J.A., Mead R. (1965); A Simplex Algorithm for Function Minimization, Computer Journal 7, 308–313.
Nocedal J., Wright S.J. (1999); Numerical Optimization, Springer, New York.
## garchSpec - spec = garchSpec() spec ## garchSim - x = garchSim(model = spec@model, n = 500) head(x) ## garchFit - # fit = garchFit(~garch(1, 1), data = x) # print(fit) ## Interactive Plot: ## plot(fit) ## Batch Plot: # plot(fit, which = 3) # summary(fit)