Bollerslev and Mikkelson(1996) FIEGARCH Model

[Arife Ozdemir]

Hello Tom,
We did according to gaussian max likelihood in FIEGARCH model, Which approach was used to estimate the FIEGARCH model? Which distribution did you use? Can we use student-t or GED distribution or skewt-t ? Is the t distribution used in the FIEGARCH model? If we want to change distributions, what should we change in the formula? If we make diagnostic tests like koutmoss (1996), Can it work in FIEGARCH model? How to make diagnostic tests on the FIEGARCH model?

[TomDoan]

Hello Tom,
We did according to gaussian max likelihood in FIEGARCH model, Which approach was used to estimate the FIEGARCH model? Which distribution did you use?

I'm not sure what you're asking. Gaussian maximum likelihood means Normal distribution. Which is what the example uses.

Can we use student-t or GED distribution or skewt-t ? Is the t distribution used in the FIEGARCH model? If we want to change distributions, what should we change in the formula?

You can. The t requires adding the shape parameter to the parameter set, and using %logtdensity(h,u,nu) in place of %logdensity(h,u). GED can be used, but there is no real point to it.

If we make diagnostic tests like koutmoss (1996), Can it work in FIEGARCH model? How to make diagnostic tests on the FIEGARCH model?

Yes. The standardized residuals can be computed as

set stdu = u/sqrt(h)

and you can do diagnostics on that.

I would note, however, that this is really a bad model to employ. Two people could take the same data set, change the truncation point of the fractional expansion and get completely different answers. Not differing in the second decimal place---completely different. The recursion takes too long to stabilize to be useful in practice.

[Arife Ozdemir]

Hello Tom, I have a new question about FIGARCH model. I would like to add a dummy variable to remove the effect of structural breaks in the Fıgarch model. How can I incorporate a dummy variable in a FIGARCH model? I tried but could not. I would be very happy if you could help me. Thank you very much in advance..

[TomDoan]

What did you try that didn't work?

[Arife Ozdemir]

we would like to investigate the long memory of volatility in S & P 500 index Using the work of Baillie vd. (1996) "Fractionally integrated generalized autoregressive conditional heteroskedasticity ". How to add 2008 global crisis as a dummy variable to FIGARCH formulation. How can we look at whether the global crisis has a meaningful effect as a parameter

[TomDoan]

"I tried but could not". What did you try that didn't work?

[Arife Ozdemir]

How do I insert a dummy variable into the following code. I do not know how to add.



nonlin(parmset=garchparms) c b d
set uufilter = 0.0
function %uufilter d
type real d %uufilter
set u = r-meanf
set uu = u^2
if d>1.0.or.d<0.0
set uufilter = %na
else
diff(fraction=d,pad=uupresample) uu / uufilter
end
compute c=uupresample*.1,b=0.7,d=.8
frml varf = c+b*h{1}+uu-b*uu{1}-uufilter
frml logl = (h(t)=varf(t)),%logdensity(h,u)
maximize(startup=%uufilter(d),parmset=meanparms+garchparms,$
title="FIGARCH(1,d,0)") logl gstart *
set ustd gstart * = u/sqrt(h)

[TomDoan]

That depends upon what you mean. If you look at the FIEGARCH paper, they include a non-trading days dummy which they interpret as having an additive effect on the variance. That requires placing the shift information in several places to achieve the desired effect. You could also simply replace the C in the VARF with C plus another free parameter times your dummy for an innovational (gradual) effect.