GarchModelling {fSeries}R Documentation

Univariate GARCH Time Series Modelling

Description

A collection and description of functions to simulate artificial ARCH time series processes, to fit the parameters of univariate time series to ARCH models, to perform a diagnostic analysis of the fit, and to predict future values of the time series.

The family of GARCH time series models includes the following processes:

garch generalized AR conditional heteroskedastic models,
aparch asymmetretic power ARCH models.

Note: This collection is still under a complete reconstruction.

Usage

garchSpec(model = list(omega = 1.0e-6, alpha = 0.1, beta = 0.8), 
        presample = NULL, cond.dist = c("rnorm", "rged", "rstd", "rsnorm", 
        "rsged", "rsstd"))
## S3 method for class 'garchSpec':
print(x, ...)

garchSim(model = list(omega = 1.0e-6, alpha = 0.1, beta = 0.8), n = 100, 
        presample = NULL, cond.dist = c("rnorm", "rged", "rstd", "rsnorm", 
        "rsged", "rsstd"))

garchFit(formula.mean = ~arma(0, 0), formula.var = ~garch(1, 1), 
        series = x, presample =  NULL, 
        cond.dist = c("dnorm", "dged", "dstd", "dsnorm", "dsged", "dsstd"), 
        symmetric = TRUE, trace = TRUE, title = NULL, description = NULL, ...)
## S3 method for class 'fGARCH':
print(x, ...)
## S3 method for class 'fGARCH':
plot(x, ...)
## S3 method for class 'fGARCH':
summary(object, ...)

Arguments

cond.dist [garchSpec, garchSim, garchFit] -
a character string naming the desired conditional distribution. Valid values are "dnorm", "dged", "dstd", "dsnorm", "dsged", "dsstd". The default value is the normal distribution.
description [garchFit] -
a character string which allows for a brief description.
formula.mean, formula.var [garchFit] -
two formula objects describing the mean and variance equation of the ARMA-GARCH/APARCH model. By default a pure GARCH(1,1) mode is selected, this means: formula.mean=~arma(0,0), and formula.var=~garch(1,1). To specify for example an APARCH(1,1) use: formula.var=~apaarch(1,1)
model [garchSpec, garchSim] -
List of GARCH model parameters:
omega - the constant coefficient of the variance equation;
alpha - the vector of autoregressive coefficients;
beta - the vector of variance coefficients;
Further Optional Values:
mu - the mean value;
ar - the autoregressive ARMA coefficients;
ma - the moving average ARMA coefficients;

The default model is Bollerslev's GARCH(1,1) model.
n [garchSim] -
length of output series, an integer value. An integer value, by default n=100.
object [summary] -
an object of class fGARCH as returned from the function garchFit().
presample a numeric three column matrix with start values for the series, innovations, and conditional variances. For an ARMA(m,n)-GARCH(p,q) process the number of rows must be at least max(m,n,p,q), longer presamples are cutted.
series [garchFit] -
a numeric vector or univariate timeSeries object to be fitted. By default series=x.
symmetric a logical flag for APARCH models. Should the model be leveraged? By default symmetric=TRUE.
title [garchFit] -
a character string which allows for a project title.
trace [garchFit] -
a logical flag. Should the optimization process of fitting the model parameters be printed. By default trace=TRUE.
x [print][plot] -
either an object of class garchSpec for printing specification structures, or an object of class fGARCH for printing fitted GARCH/APARCH models or plotting results from the diagnostic analysis of fitted models.
... additional arguments to be passed.

Details

Parameter Estimation:

garchFit uses the nlminb() optimizer to find the maximum likelihood estimates.

Value

garchSpec

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 for the mean and variance equation.
@model a list with the model parameters.
@presample a numeric matrix with presample values.
@distribution a character string with the name of the conditional distribution.
@call the call of the garch function.
@formula a list with two formula entries for the mean and variance equation.
@method a string denoting the optimization method.
@fit a list with the results from the parameter estimation.
@residuals a numeric vector with the residual values.
@fitted.values a numeric vector with the fitted values.
@title a title string.
@description a string with a brief description.

Author(s)

Diethelm Wuertz for the Rmetrics R-port.

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.

Engle R.F. (1982); Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica 50, 987–1008.

Examples

## SOURCE("fSeries1.34C-GarchModelling")
## Not run: 
#       garchSpec -
#   garchSim - 
#       garchFit -

    # For examples we refer to: demo/xmpDWChapter34.R ...
## End(Not run)

[Package fSeries version 220.10063 Index]