Bivariate Garch Model with dummy and interactions

[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.

[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

[TomDoan]

Those are definitely not standardized---the recursion is in terms of the covariance matrices themselves.

[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

[TomDoan]

You standardize residuals for doing diagnostics. VIRF's (or forecasts) work with the actual data and variances.

[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

[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".

[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

[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.

[Lena]

Thank you Tom for making this clear!
I very much appreciate it!

Best
Lena