GEVStableGarch-package:
ARMA-GARCH/APARCH modelling with GEV and stable distributions

Description

This package is designed to perform maximum likelihood estimation of ARMA-GARCH/APARCH models with generalized extreme distribution (GEV), stable, generalized asymmetric t (GAt) and skew Student's t from Fernandez and Steel (1998). The package also allows the researcher to restrict the search within the stationarity region (see the gsFit function). Other common conditional distribution (normal, Student's t and generalized error distribution (GED)) are also allowed since they are very important for testing purposes.

Arguments

Time Series Simulation

Contains functions to simulate ARMA-GARCH/APARCH processes with conditional GEV or stable distributions. Note: These routines were adapted from functions garchSpec and garchSim available in fGarch package to make the interfaces more similar. Functions:

gsSpec

Specifies an univariate ARMA-GARCH/APARCH model,

Parameter Estimation

Contains functions to fit the parameters of ARMA-GARCH/APARCH time series processes. Functions:

gsFit Fits the parameters of an ARMA-GARCH/APARCH process.

This function also provides an algorithm to enforce stationarity during estimation,

Other Conditional Distribution Functions

Contains functions to compute density, distribution, quantiles and generate random values using important conditional distributions used in the garch literature. Functions:

[dpqr]skstd Skew Student's t distribution function from Fernandez and Steel (1998),

[dpqr]gat Generalized Asymmetric t distribution (GAt).

The GAt distribution was also refered in the literature as t3-distribution.

gsMomentAparch Computes APARCH Moments of the form $E( |Z| - \gamma Z ) ^ \delta$ for several distributions

Details

Package:

GEVStableGarch

Type:

Package

Version:

1.1

Date:

2015-07-19

License:

GPL(>=2)

Depends:

R(>= 2.15.0), fGarch, fExtremes, stabledist, skewt, Rsolnp

GARCH models have proven to be highly effective for analyzing financial data over the past decades. In particular, the combination of ARMA-GARCH models with stable and GEV distributions was successfully applied for forecasting volatility and for the measurement of Value at Risk (VAR).

Choosing the normal distribution as probability distribution for the innovations was a common choice in the beginning of the development of ARCH-type models. But recent research Nolan (1999), Mittnik et al. (2002), Mittnik and Paolella (2003), Curto et al. (2006), Frain (2009), Zhao et al. (2011) has shown that other distributions should be considered, specially because normal distribution can not account for fat tails and asymmetry found in real data.

This package contains functions for simulating and estimating ARMA-GARCH or ARMA-APARCH models using the maximum likelihood technique (MLE) under different assumptions: GEV, stable, GAt (also known as t3-distribution) and skew Student's t (Fernandez and Steel (1998)).