Modelling heterskedasticity in financial time series
The Rmetrics fGarch package is a collection of functions to analyze and model heteroskedastic behavior in financial time series.
package
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 georgi.boshnakov@manchester.ac.uk
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.
Functions to simulate artificial GARCH and APARCH time series processes.
garchSpec | specifies an univariate GARCH time series model |
garchSim | simulates a GARCH/APARCH process |
Functions to fit the parameters of GARCH and APARCH time series processes.
garchFit | fits the parameters of a GARCH process |
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 |
Functions to forcecast mean and variance of GARCH and APARCH processes.
predict | forecasts from an object of class "fGARCH" |
This section contains functions to model standardized distributions.
[dpqr]norm | Normal distribution (base R) |
[dpqr]snorm | Skew normal distribution |
snormFit | fits parameters of Skew normal 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 |
[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 |
absMoments | computes absolute moments of these distribution |
The fGarch Rmetrics package is written for educational support in teaching "Computational Finance and Financial Engineering" and licensed under the GPL.
Useful links