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The Rmetrics fGarch package is a collection of functions to analyze and model heteroskedastic behavior in financial time series.


Diethelm Wuertz [aut] (original code), Yohan Chalabi [aut], Tobias Setz [aut], Martin Maechler [ctb] (<>), Chris Boudt [ctb] Pierre Chausse [ctb], Michal Miklovac [ctb], Georgi N. Boshnakov [cre, ctb]

Maintainer: Georgi N. Boshnakov <>

1 Introduction

GARCH, Generalized Autoregressive Conditional Heteroskedastic, models have become important in the analysis of time series data, particularly in financial applications when the goal is to analyze and forecast volatility.

For this purpose, the family of GARCH functions offers functions for simulating, estimating and forecasting various univariate GARCH-type time series models in the conditional variance and an ARMA specification in the conditional mean. The function garchFit is a numerical implementation of the maximum log-likelihood approach under different assumptions, Normal, Student-t, GED errors or their skewed versions. The parameter estimates are checked by several diagnostic analysis tools including graphical features and hypothesis tests. Functions to compute n-step ahead forecasts of both the conditional mean and variance are also available.

The number of GARCH models is immense, but the most influential models were the first. Beside the standard ARCH model introduced by Engle [1982] and the GARCH model introduced by Bollerslev [1986], the function garchFit also includes the more general class of asymmetric power ARCH models, named APARCH, introduced by Ding, Granger and Engle [1993]. The APARCH models include as special cases the TS-GARCH model of Taylor [1986] and Schwert [1989], the GJR-GARCH model of Glosten, Jaganathan, and Runkle [1993], the T-ARCH model of Zakoian [1993], the N-ARCH model of Higgins and Bera [1992], and the Log-ARCH model of Geweke [1986] and Pentula [1986].

There exist a collection of review articles by Bollerslev, Chou and Kroner [1992], Bera and Higgins [1993], Bollerslev, Engle and Nelson [1994], Engle [2001], Engle and Patton [2001], and Li, Ling and McAleer [2002] which give a good overview of the scope of the research.

2 Time series simulation

Functions to simulate artificial GARCH and APARCH time series processes.

garchSpecspecifies an univariate GARCH time series model
garchSimsimulates a GARCH/APARCH process

3 Parameter estimation

Functions to fit the parameters of GARCH and APARCH time series processes.

garchFitfits the parameters of a GARCH process

Extractor Functions:

residualsextracts residuals from a fitted "fGARCH" object
fittedextracts fitted values from a fitted "fGARCH" object
volatilityextracts conditional volatility from a fitted "fGARCH" object
coefextracts coefficients from a fitted "fGARCH" object
formulaextracts formula expression from a fitted "fGARCH" object

4 Forecasting

Functions to forcecast mean and variance of GARCH and APARCH processes.

predictforecasts from an object of class "fGARCH"

5 Standardized distributions

This section contains functions to model standardized distributions.

Skew normal distribution:

[dpqr]normNormal distribution (base R)
[dpqr]snormSkew normal distribution
snormFitfits parameters of Skew normal distribution

Skew generalized error distribution:

[dpqr]gedGeneralized error distribution
[dpqr]sgedSkew Generalized error distribution
gedFitfits parameters of Generalized error distribution
sgedFitfits parameters of Skew generalized error distribution

Skew standardized Student-t distribution:

[dpqr]stdStandardized Student-t distribution
[dpqr]sstdSkew standardized Student-t distribution
stdFitfits parameters of Standardized Student-t distribution
sstdFitfits parameters of Skew standardized Student-t distribution

Absolute moments:

absMomentscomputes absolute moments of these distribution

About Rmetrics

The fGarch Rmetrics package is written for educational support in teaching "Computational Finance and Financial Engineering" and licensed under the GPL.