Hi,
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?



Thanks a lot for your help to clarify this!


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