ruGARCH realGARCH: Comparing sigma() with realizedVol input

Hi Alexios,

Thanks for the fast reply, to answer your questions:

Did you first try a (1,1)-Normal model? Yes- I did try simpler models
and its the same story. I also used the data you use on your blog
(spyreal) and found that the fitted and underlying measure are
'overlapping'. So in the spyreal data there is no structural difference
as there is in my data.

Did you expect them to have the same values?  I was actually not sure
whether to expect fitted sigma and realizedVol measure to have the same
value. This was part of my question. But given that you say that
realGARCH is first and foremost an GARCH model augmented with the
realized measure, - I guess I should not expect them to have the same
value. As I understand you now, realGARCH is not a model for the
realized measure (which is what I was after).

Regards,
Duco

Subject: Re: [R-SIG-Finance] ruGARCH realGARCH: Comparing sigma() with

realizedVol input

From: alexios at 4dscape.com
Date: Mon, 17 Feb 2014 10:49:53 +0000
CC: alexios at 4dscape.com; r-sig-finance at r-project.org
To: ducovrossem at hotmail.com

Did you expect them to have the same values? This is first and

foremost a GARCH model augmented with the realized measure. Did you read
the blog post and vignette first?

Beyond that, it is difficult to comment without looking at your data

(reproducible code).

Did you first try a (1,1)-Normal model (to compare the likelihoods in

case the model converged to a non-global optimum)?

-Alexios

On 17 Feb 2014, at 10:30, Duco van Rossem <ducovrossem at hotmail.com> wrote:

Dear list,
I am trying to compare the fitted sigma of the realGARCH model with

my realized volatility input. However these two time series have
completely different values. My realizedVol input has a values of around
0.004-0.010, while the fitted sigma output has values of around
0.001-0.003 and I am trying to understand why.

Below I walk through my code:
My model specification fitting below, where,return_c2casxts - daily

close-to-close return object (an xts object)RVar_BN2008 - Daily realized
variance measure (using realized kernel of Bandorff Nielsen 2008)

spec.realGARCH21 <- ugarchspec(variance.model = list(model =

"realGARCH", garchOrder = c(2,1)), mean.model = list(armaOrder =
c(1,1)), distribution.model =
"std")garch_model<-ugarchfit(spec.realGARCH21, return_c2casxts, solver =
'hybrid', realizedVol=sqrt(RVar_BN2008))

RVolfitted<-garch_model at fit$sigma

Now comparing RVolfitted and sqrt(RVar_BN2008)below I have

completely different values throughput the series (3500 days in total).

RVolfitted:" 0.0020383691 0.0018783530 0.0020688548 0.0015357892

0.0016052453 0.0016191145sqrt(RVar_BN2008): 0.006596078 0.008683373
0.004344591 0.006393453 0.006223041 0.008463817

Is this a conceptual issue on my part on what sigma signifies here?

How can I obtain fitted values corresponding to the realizedVol input?

Best Regards,Duco
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