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)