[R-SIG-Finance] Question about garchSim and garch

[Spencer Graves]

Hi, Tom: 

      The file 'scripts\ch03.R' in the FinTS package includes a brief 
description of attempts to use garch{tseries} and garchFit{fGarch}.  I 
don't understand either function very well, but I got answers from 
'garchFit' that seemed to match some of the published results in Tsay;  
I gave up on 'garch'. 

      Since 'garchSim' and 'garchFit' are both in 'fGarch', I would 
expect that it should be moderately easy to simulate something, plot the 
result, and see for yourself.  Chapter 3 of Tsay (2005) gives a 
reasonable overview of GARCH and related models with several examples.  
The companion script\ch03.R is far from complete but might help. 

      You may find the following example from 'ch03.R' of interest: 

library(FinTS)
data(sp500)
library(fGarch)
spFit30.11 <- garchFit(sp500~arma(3,0)+garch(1,1), data=sp500)

      This specifies an arma(3,0) mean model with garch(1,1) noise.  
This syntax is buried in the 'garchFit' help page. 

      Hope this helps. 
      Spencer

tom soyer wrote:
> Hi,
>
> I am new to GARCH and I am trying to figure out how to use R's garchSim and
> garch, and I am a bit confused. I am hopeing that R finance experts can help
> me understand them better. If we look at the definition of GARCH(1,1),
> there should be two equations:
> [1]: Y(t) = c + e(t), and
> [2]: sigma^2(t) = a0 + a1*e^2(t-1) + b1*sigma^2(t-1)
>
> So, I would expect any garch simulation function to four parameters: c, a0,
> a1, and b1. But take a look at the garchSim, it has only three parameters:
> model = list(omega = 1.0e-6, alpha = 0.1, beta = 0.8). I assume here that
> omega = a0 in [2], alpha=a1, and beta=b1. If so, then it seems that in
> garchSim, c, the constant (or the mean) in [1], is always assumed to be
> zero. Does anyone know if this is true? I just want to make sure that I
> understand exactly what I should expect from the output of the garchSim
> function.
>
> Also, I have a similar question about garch. It seems that the coefficients
> estimated by garch(x,order=c(1,1)) are a0, a1, and b1. Like garchSim, there
> is no c, the mean. So does this mean garch also assumes zero mean and thus
> actually fits model [2] instead of both [1] and [2]?
>
> Thanks!
>
>