[R-SIG-Finance] Parameterization of the GED distribution in rugarch package - second try

[Maxim Odulero]

Ok,
I was told to post under my real name I hereby do this from my gmail account.

I have the second mail adress (copulaguy at yahoo.de), because I
sometimes post in (german & non-german) forums/q&a sites questions
concerning the topic copula. I ask this specific question to this R
list, since it is a specific one (no, I did not post this somewhere
else). Once again my post, an answer would be appreciated! Thanks!

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I am wondering about the following:

When I use the rugarch package I can get the ugarchroll output,
showing me the mean, sigma, shape, skew shape(GIG) and realized
values. I understand, that these are the 1 step ahead forecasted
values. So I can then apply the plot function applied to it and choose
the first plot, which shows me the one step ahead forecasted
densities. The forecasted density is determined by the values give in
the output, i.e. it uses the mean, the variance and the other
estimates (shape parameter and so) to draw the different densities.


I used the generalized error distribution in my model specification.
According to the rugarch manual page 15 you an see, that this
distribution is determined by three parameters: The location, scale
and shape parameter. So I need three values to draw the density. Now
my question is the following:

>From the output table (of ugrachroll) I can see, that I have estimates
for the mu sigma and shape. I think, that the mu estimate is exactly
the location parameter. The shape parameter is also clear to me. Now I
am not getting the following: What is the sigma?

Is this the estimate for the scale parameter beta or is it an estimate
of the standard deviation?

If it is an estimate of the standard deviation, that would mean
according to fomula 55, that I have to plug in the squared value to
the left and the shape esimtate to the right and then solve for the
beta parameter to get the right parameter and to be able to draw the
density? Is this right?

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Maxim