GEVStableGarch (version 1.1)

gsSim: Simulation of ARMA-GARCH/APARCH process

Description

This functions simulates time series following ARMA-GARCH/APARCH models with GEV and stable distributions. This function was developed through the available code from fGarch package available at CRAN.

Usage

gsSim(spec = gsSpec(), n = 100, n.start = 100)

Arguments

spec

A model specified with function gsSpec.

n

The size of simulated time series.

n.start

Length of the "burn-in" period of the simulated time series.

Value

The function returns an object containing the following items:

model

A string describing the estimated model.

cond.dist

The conditional distribution used to fit the model.

series

An array with three columns, where the first column contains the simulated ARMA-GARCH/APARCH process (garch), the second column the conditional standard deviations ("sigma"), and the last column the innovations ("eps").

Details

The initial values of the time series are fixed and the recursion formulas of the model are used to simulate the dynamics of the process. We do not verify the stationarity conditions of the model because the simulation of non-stationary process could also be of interest by the researcher.

References

Brockwell, P.J., Davis, R.A. (1996). Introduction to Time Series and Forecasting. Springer, New York.

Wuertz, D., Chalabi, Y., with contribution from Miklovic, M., Boudt, C., Chausse, P., and others (2013). fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling, R package version 3010.82, http://CRAN.R-project.org/package=fGarch.

Wuertz, D., Chalabi, Y., Luksan, L. (2009). Parameter Estimation of ARMA Models with GARCH/ APARCH Errors: An R and SPlus SoftwareImplementation. Journal of Statistical Software, forthcoming, http://www-stat.wharton.upenn.edu/~steele/...WurtzEtAlGarch.pdf.

Examples

# Simulation of a ARMA-APARCH process with stable conditional distribution
#x <- GSgarch.Sim(N = 2500, mu = 0.1,a = c(0.2,0.3),b = c(0.2,0.5),
#omega = 0.1, alpha = c(0.1,0.2),beta = c(0.1,0.1),gm=c(0.3,-0.3),
#delta = 1,skew = 0.3,shape = 1.9, cond.dis = "stable")