TSA (version 1.3)

garch.sim: Simulate a GARCH process

Description

Simulate a GARCH process.

Usage

garch.sim(alpha, beta, n = 100, rnd = rnorm, ntrans = 100,...)

Arguments

alpha

The vector of ARCH coefficients including the intercept term as the first element

beta

The vector of GARCH coefficients

n

sample size

rnd

random number generator for the noise; default is normal

ntrans

burn-in size, i.e. number of initial simulated data to be discarded

...

parameters to be passed to the random number generator

Value

simulated GARCH time series of size n.

Details

Simulate data from the GARCH(p,q) model: \(x_t=\sigma_{t|t-1} e_t\) where \(\{e_t\}\) is iid, \(e_t\) independent of past \(x_{t-s}, s=1,2,\ldots\), and $$\sigma_{t|t-1}=\sum_{j=1}^p \beta_j \sigma_{t-j|t-j-1}+ \alpha_0+\sum_{j=1}^q \alpha_j x_{t-i}^2$$

Examples

# NOT RUN {
set.seed(1235678)
garch01.sim=garch.sim(alpha=c(.01,.9),n=500)
plot(garch01.sim,type='l', main='',ylab=expression(r[t]),xlab='t')
# }