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Re: Bivariate Garch Model with dummy and interactions
Posted: Wed Dec 14, 2016 7:44 am
by TomDoan
Yes. The %%VAR_A and %%VAR_B matrices that are used in the recursion need to be pulled out of your parameter set rather than out of the GARCH output.
Re: Bivariate Garch Model with dummy and interactions
Posted: Tue Apr 04, 2017 7:35 am
by Lena
Dear Tom,
althought I figured out how to estimate the VIRF's (thanks to your help!!!) I just realized that I never standardized the residuals to get identical and idenpendent shocks.
So I tried to understand what you did in your GARCHMODELS.RPF procedure.
In your example
Code: Select all
* Black Wednesday shocks. These are computed using a baseline of the
* estimated volatility state, so they are excess over the predicted
* covariance.
*
compute eps0=rv(blackwed)
compute sigma0=hh(blackwed)
compute shock=1.e+4*%vec(%outerxx(eps0)-sigma0)
you use the residuals rv. But these aren't the standardized ones, or are they? And if not, how do I standardize them?
Thanks for your very helpful support!
Best
Lena
Re: Bivariate Garch Model with dummy and interactions
Posted: Wed Apr 05, 2017 10:44 am
by TomDoan
Those are definitely not standardized---the recursion is in terms of the covariance matrices themselves.
Re: Bivariate Garch Model with dummy and interactions
Posted: Thu Apr 06, 2017 3:57 am
by Lena
That's what I thought. I figured out, that you standardize the residuals by using the J-B test which (I suppose) saves them in v.
But still, why don't you use them in your calculation of the VIRF's?
Best
Lena
Re: Bivariate Garch Model with dummy and interactions
Posted: Thu Apr 06, 2017 7:38 am
by TomDoan
You standardize residuals for doing diagnostics. VIRF's (or forecasts) work with the actual data and variances.
Re: Bivariate Garch Model with dummy and interactions
Posted: Thu Apr 06, 2017 11:17 am
by Lena
Thank you Tom!
But as far as I understand Hafner and Herwartz (2006) paper, they use Jordan decomposition to
avoid typical orthogonalization and ordering problems. So if I use the actual data for my VIRF's wouldn't it be than necessary to calculate the "inital" shock afterwards?
Sorry for bothering you with this!!
Lena
Re: Bivariate Garch Model with dummy and interactions
Posted: Thu Apr 06, 2017 11:50 am
by TomDoan
Yes, that is a somewhat confusing part of the paper. They are trying to define an atheoretical measurement of the "news". However, it doesn't matter how you break down the residuals at the T0 if you make no attempt to isolate the specific parts of it---their VIRF calculation takes the entire outer product of the residual as the variance "shock".
Re: Bivariate Garch Model with dummy and interactions
Posted: Thu Apr 06, 2017 1:14 pm
by Lena
Thanks Tom, I'm not 100% sure if I got your point since a lot of other papers in wich VIRF's are used also refer to the Jordan Decomposition but I will think about it!
At least I know that everything is fine with my calculation!
Best
Lena
Re: Bivariate Garch Model with dummy and interactions
Posted: Thu Apr 06, 2017 1:28 pm
by TomDoan
What they're describing is actually the symmetric square root which is one of several order- and model-free methods of factoring a covariance matrix. I'm going to guess that the other papers simply copied most of the discussion from the HH paper. Basically, they have a page of algebra to show that the factorization cancels when you are looking at the effect going forward of the residuals at a given historical episode.
The problem with the symmetric square root is that, as a result of being model-free, it's also content-free. Thus it would make no sense to take one "independent" piece of information generated using it and see what the effect is in isolation, since you can't really make any sense out of the "news" that it represents, thus the use of the entire residual.
Re: Bivariate Garch Model with dummy and interactions
Posted: Fri Apr 07, 2017 1:09 am
by Lena
Thank you Tom for making this clear!
I very much appreciate it!
Best
Lena