fGarch (version 260.72)

GarchFitting: Univariate GARCH Time Series Fitting

Description

Estimates the parameters of an univariate GARCH process.

Usage

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)

Arguments

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

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 arma

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 f

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

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.

Value

• 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.

References

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.

Examples

## 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)