00fGarch-package: Modelling heterskedasticity in financial time series

In fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling

Modelling heterskedasticity in financial time series

Description

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

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.

garchSpec	specifies an univariate GARCH time series model
garchSim	simulates a GARCH/APARCH process

3 Parameter estimation

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

garchFit

fits the parameters of a GARCH process

Extractor Functions:

residuals	extracts residuals from a fitted "fGARCH" object
fitted	extracts fitted values from a fitted "fGARCH" object
volatility	extracts conditional volatility from a fitted "fGARCH" object
coef	extracts coefficients from a fitted "fGARCH" object
formula	extracts formula expression from a fitted "fGARCH" object

4 Forecasting

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

predict

forecasts from an object of class "fGARCH"

5 Standardized distributions

This section contains functions to model standardized distributions.

Skew normal distribution:

[dpqr]norm	Normal distribution (base R)
[dpqr]snorm	Skew normal distribution
snormFit	fits parameters of Skew normal distribution

Skew generalized error distribution:

[dpqr]ged	Generalized error distribution
[dpqr]sged	Skew Generalized error distribution
gedFit	fits parameters of Generalized error distribution
sgedFit	fits parameters of Skew generalized error distribution

Skew standardized Student-t distribution:

[dpqr]std	Standardized Student-t distribution
[dpqr]sstd	Skew standardized Student-t distribution
stdFit	fits parameters of Standardized Student-t distribution
sstdFit	fits parameters of Skew standardized Student-t distribution

Absolute moments:

absMoments

computes 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.

Author(s)

Diethelm Wuertz [aut] (original code), Yohan Chalabi [aut], Tobias Setz [aut], Martin Maechler [ctb] (<https://orcid.org/0000-0002-8685-9910>), Chris Boudt [ctb] Pierre Chausse [ctb], Michal Miklovac [ctb], Georgi N. Boshnakov [cre, ctb]

Maintainer: Georgi N. Boshnakov <[e-mail]>

fGarch documentation built on Oct. 15, 2023, 5:06 p.m.