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

[Patrick Burns]

tom soyer wrote:

>Thnaks Spencer. I am glad I am not the only one that find garch strange. I
>guess I will give up on it too. It seems that garchFit and garchSim are very
>good. They have been giving me good results so far.
>
>Thanks for the tip on how to specify arma + garch model. I found this paper
>also very helpful:http://www.itp.phys.ethz.ch/econophysics/R/pdf/garch.pdf.
>
>Do you know how to specify arma + egarch model in R? Is it even possible in
>R without installing Ox?
>  
>

In my experience ARMA estimation and garch estimation are
suitably robust to each other.  It is definitely second prize to have
to estimate one and then the other, but your results are unlikely to
be all that different than if you did it "right".  (I'd love to hear of
any counter-examples.)

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")

>
>On 2/2/08, Spencer Graves <spencer.graves at pdf.com> wrote:
>  
>
>>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!
>>>
>>>
>>>      
>>>
>
>
>
>  
>