R help - Jun 2009 - using garchFit() to fit ARMA+GARCH model with exogeneous variables

Hello -
 
Here's what I'm trying to do. I want to fit a time series y with
ARMA(1,1) + GARCH(1,1), there are also an exogeneous variable x which I
wish to include, so the whole equation looks like:
 
y_t - \phi y_{t-1} = \sigma_t \epsilon_t + \theta \sigma_{t-1}
\epsilon_{t-1} + c x_t       where \epsilon_t are i.i.d. random
variables
 
\sigma_t^2 = omega + \alpha \sigma_{t-1}^2 + \beta y_{t-1}^2
 
 
I looked through documentation of garchFit() from the fGarch library but
didn't find a way to include exogeneous variables like x_t. How do I do
that? Thank you very much in advance!
 
Yuhan Zhang
Morgan Stanley | Fixed Income
1585 Broadway, 3rd Floor | New York, NY  10036
Phone: +1 212 761-2313
Yuhan.Zhang@morganstanley.com

 

--------------------------------------------------------------------------
This is not an offer (or solicitation of an offer) to bu...{{dropped:24}}

Hello, Yuhan: 


      If I wanted to get something sensible today, I'd do ordinary least 
squares using lm(y~x), the garchFit on the residuals.  This will give 
you a reasonable answer except that the confidence intervals from "lm"
will not be accurate.  I'd want to do normal probability plots of the 
residuals and whitened residuals.  Then I might also do a Monte Carlo to 
evaluate the distribution of paramter estim


      If I wanted to go beyond this, I might write my own likelihood 
function and use, e.g., the maxLik package to get the MLEs, etc. 


      However before I did that, I would do a more careful search of 
capabilities in contributed packages, something like the following: 


library(RSiteSearch) # to search help pages of contributed packagee
gar <- RSiteSearch.function('GARCH') # for GARCH
HTML(gar) # to display the results in a web browser
ar <- RSiteSearch.function('ARMA') # Search for ARMA
ari <- RSiteSearch.function('ARIMA') # or ARIMA
ar. <- ar|ari # for help pages containing either ARMA or ARIMA
ar.gar <- ar.&gar # for help pages containing both ARMA / ARIMA and GARCH
summary(ar.gar) # to display the packages
ArG <- PackageSum2(ar.gar) # for a summary with more detail on installed 
packages
write.csv(ArG, 'ArG.csv') # written to a CSV file where it can more 
easily be displayed and modified, e.g., in MS Excel
HTML(ar.gar) # To display the results in a web browser.  


      This search did not produce much for me, which is part of the 
reason I suggested maxLik. 


      Hope this helps. 
      Spencer Graves


Zhang, Yuhan wrote:
> Hello -
>  
> Here's what I'm trying to do. I want to fit a time series y with
> ARMA(1,1) + GARCH(1,1), there are also an exogeneous variable x which I
> wish to include, so the whole equation looks like:
>  
> y_t - \phi y_{t-1} = \sigma_t \epsilon_t + \theta \sigma_{t-1}
> \epsilon_{t-1} + c x_t       where \epsilon_t are i.i.d. random
> variables
>  
> \sigma_t^2 = omega + \alpha \sigma_{t-1}^2 + \beta y_{t-1}^2
>  
>  
> I looked through documentation of garchFit() from the fGarch library but
> didn't find a way to include exogeneous variables like x_t. How do I do
> that? Thank you very much in advance!
>  
> Yuhan Zhang
> Morgan Stanley | Fixed Income
> 1585 Broadway, 3rd Floor | New York, NY  10036
> Phone: +1 212 761-2313
> Yuhan.Zhang at morganstanley.com
>
>  
>
> --------------------------------------------------------------------------
> This is not an offer (or solicitation of an offer) to bu...{{dropped:24}}
>
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