cf_mstr


Total Posts: 10 
Joined: Aug 2016 


Hi all, simple question:
For a GARCH type model fitting, when we do the JarqueBera test to confirm our data does not have a Gaussian distribution, we then use the Quasimaximum likelihood estimation for our parameters optimization. The formula I have for it is this:
Where gamma (r) is a gamma function (r(n)=(n1)!) , squared sigma our conditional variance and epsilon the log return of the period. So from what I understand, Nu (v) is our degree of freedom, that we also optimize. For out of sample usage, we optimize Nu at each step before optimizing our model parameters. Is this correct? 



cf_mstr


Total Posts: 10 
Joined: Aug 2016 


Also, instead of using a Studentt, we can use a generalized normal distribution. My understanding is that both will have practically the same performance. Is that right?
Thanks 


cf_mstr


Total Posts: 10 
Joined: Aug 2016 


I am guessing that the phynance GOD that is able to answer those questions could also answer this one:
I am using a GARCH (1,1) model for 04 jan 2010 to 08 dec 2015 of EURUSD daily close log return data.
The data distribution is clearly not normal (kurtosis=4.53, skewness=0.27, JarqueBera test statistic= 132)
QQ plot:
When estimating the parameters with MLE, we have a=0.0416 b=0.9568 w=1.51E07 MLE=4306
Then, I want to use a QMLE with GED as follow:




cf_mstr


Total Posts: 10 
Joined: Aug 2016 


Asking this question in two posts since there seem to be a problem. When I post it as one message it cuts out parts. I am guessing it has something to do with the screenshots.
Anyway here's the rest of the question:
When v = 2, we have a standard normal distribution. When v is less than 2, we have a distribution with thicker tails. As mentioned by Nelson (1991) (Conditional Heteroskedasticity in Asset Returns: A New Approach)
However, when I optimize the degrees of freedom, it gives v = 3.66 Then optimizing parameters we have a=0.0396 b=0.9604 w=4.72E07 QMLE=6188
The optimization result for the degree of freedom doesn't make sense to me. If the data distribution is leptokurtic, shouldn't the optimal degree of freedom reflect that and be less than 2 ?
Also note: When estimating parameters with QMLE, v=2, the results are the same as when estimating with MLE, which tells me that my formulas are probably good 

