[R-SIG-Finance] Q: SGT for GARCH estimation

[Alex Garland]

Enjo,

I'm more than willing to be corrected on these matters, but if I were 
you, I would immediately see moving forward in one of three ways: two of 
which are technically easy but not what you want per se, and the other 
is conceptually easy but is exactly what you want.

The technically easy thing to do would be to use the generalized 
hyperbolic skew t student distribution or the skewed generalized error 
distribution, both of which may capture the dynamics you are interested 
in. The Skewed generalized error distribution is the limiting case of 
the skewed generalized t distribution.

The alternative, which will give you exactly the amount of fine grained 
control you want but will take a bit more work, is to implement the 
maximum likelihood estimation yourself. What this (usually) means is 
that you have a parameter vector β (this would include the parameters of 
your mean equation, the parameters of your volatility equation, and all 
of the parameters of the conditional distribution) that when given that 
vector, we know what standardized residuals that implies. We can then 
"score" the standardized residuals based on how they compare to what we 
have assumed the conditional distribution is, and pick the highest 
score. The canonical way of doing this is to take the (negative) log 
transformation of the likelihood and then maximize (minimize) it as a 
function of that parameter vector. Presumably the SGT package could be 
helpful with this somehow.

The above approach is something of a pain but it's a good way to get 
into the code yourself, and I did it for an undergraduate thesis myself 
a few years ago when I implemented a non-supported GARCH model. However, 
I note that this is not the point of your paper, so you may be unwilling 
to do that.

Anyone else should feel free to chime in if I've said anything wrong, 
missed anything in the rugarch documentation, or have generally made a 
fool of myself.

Best,

Alex

On 5/2/21 2:07 AM, enjo faes wrote:
> Dear all,
>
> In line of research conducted by 2 colleagues and me for our thesis this year, we want to examine “the importance higher moments: skewness and kurtosis of returns for VaR and cVaR estimation using GARCH for European Blue chips”.
>
> First of all, we would like to thank Alexios Ghalanos for the package Rugarch, which is quite impressive and nice to use and Kris Boudt for explaining it on Datacamp. Some things we would like to examine further, that is: the method of implementing SGT density distribution for GARCH models. I know that there is the r package SGT. But the practical way of implementing it in R with GARCH models, does not seem clear to us at this point in time.
>
> We look forward hearing from you. This is the first time I used the R-SIG-Finance list, so any comments are welcome for improvement.
>
> Best regards,
> Enjo Faes
>
>
>
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