5:34 p.m.
Hello,
I'm writing a master thesis about volatility forecasting using GARCH and
GJR models (with Normal, stud-t and GED distributions). I need to
prepare out-of-sample forecasting for that models. Thus, I've tried to
prepare scripts using gig package.
I've got the following script for GARCH (1,1) with GED distribution:
include gig.gfn
open file.gdt
model = gig_setup(RETURN,1,const)
gig_set_dist(&model, 2)
gig_estimate(&model)
#gig_plot(&emodel)
#gig_dplot(&emodel)
series e = $uhat
series h = $h
dataset addobs 1
a0 = $coeff[2]
a1 = $coeff[3]
b1 = $coeff[4]
series hfc = h
# set future errors to their expectation
e = misszero(e)
# forecast the variance
hfc = a0 + a1 * e(-1)^2 + b1 * hfc(-1)
smpl 165 ;
print e h hfc --byobs
However, the commands series e = $uhat and series h = $h don't work. The
information is that: "The statistic you requested is not available"
I'll be really grateful if you can write me how to get 'uhat' and 'h'
series in that case. Or maybe it is some another way for preparing
out-of-sample forecasting for GARCH and GJR models.
Best regards,
Marta
6:32 p.m.
On Fri, 9 Nov 2012, Marta Szymańska wrote:
Hello,
I'm writing a master thesis about volatility forecasting using GARCH and
GJR models (with Normal, stud-t and GED distributions). I need to
prepare out-of-sample forecasting for that models. Thus, I've tried to
prepare scripts using gig package.
This should be intended as a reply to Tomasz too.
Here's a variation on your script that should work as intended:
<hansl>
include gig.gfn
open djclose.gdt
RETURN = ldiff(djclose)
model = gig_setup(RETURN,1,const)
gig_set_dist(&model, 2)
gig_estimate(&model)
series e = model["uhat"]
series hfc = model["h"]
matrix coef = model["coeff"]
a0 = coef[2]
a1 = coef[3]
# coef[4] is reserved for the asymmetry coefficient
b1 = coef[5]
# forecast the variance
dataset addobs 50
setobs 5 1980/01/02
series hfc = ok(hfc) ? hfc : a0 + (a1 + b1) * hfc(-1)
smpl 1989/09/1 ;
print hfc --byobs
gnuplot hfc time --time-series --with-lines --output=display
smpl full
</hansl>
A few comments:
* we use djclose in this example so everyone has it.
* gig is an addon, so its "products" are not accessible through "$"
variables. Instead, it uses bundles, so you may fetch them by ordinary
bundle syntax; see the User's Guide and the gig documentation
* when forecasting the variance, you don't want to use the square of the
expectation of e as a predictor of e squared (Jensen's lemma): what you
need is a predictor of e^2. If you use the expectation as your predictor,
that's precisely what h is. As a consequence, in the simple case of the
garch(1,1) model with normal errors, you just forecast h by its past
values (for more complicated models, it's not so easy).
--------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
--------------------------------------------------
7:54 p.m.
Thanks you a lot, however I'm still a little bit confused about hfc
equation.
The equation of hfc for GARCH model:
# forecast the variance
hfc = a0 + a1 * e(-1)^2 + b1 * hfc(-1)
I have got from Allin Cottrell's script from this link:
http://lists.wfu.edu/pipermail/gretl-users/2011-January/005772.html.
Moreover, I found some papers in which is it stated that for volatility
forecasting we should just keep constant parameters from our in-sample
period and add one observation to both e and h.
So, what do you suggest in GJR case, should I forecast out-of-sample
volatility using GIG equation:
h_t = omega + alpha (|e_{t-1}| - gamma e_{t-1})^2 + beta h_{t-1}
or rather the same as you suggested for GARCH model, that is:
hfc : a0 + (a1 + b1) * hfc(-1)
And btw, if I'd like to use alternative parametrization in GJR, can I just
change parameters in the coefficient matrix and forecast with that
parameters? I mean, is the volatility from model the same, no matter which
parametrization we use or not?
2012/11/9 Riccardo (Jack) Lucchetti <r.lucchetti(a)univpm.it>
On Fri, 9 Nov 2012, Marta Szymańska wrote:
Hello,
>
> I'm writing a master thesis about volatility forecasting using GARCH and
> GJR models (with Normal, stud-t and GED distributions). I need to
> prepare out-of-sample forecasting for that models. Thus, I've tried to
> prepare scripts using gig package.
>
This should be intended as a reply to Tomasz too.
Here's a variation on your script that should work as intended:
<hansl>
include gig.gfn
open djclose.gdt
RETURN = ldiff(djclose)
model = gig_setup(RETURN,1,const)
gig_set_dist(&model, 2)
gig_estimate(&model)
series e = model["uhat"]
series hfc = model["h"]
matrix coef = model["coeff"]
a0 = coef[2]
a1 = coef[3]
# coef[4] is reserved for the asymmetry coefficient
b1 = coef[5]
# forecast the variance
dataset addobs 50
setobs 5 1980/01/02
series hfc = ok(hfc) ? hfc : a0 + (a1 + b1) * hfc(-1)
smpl 1989/09/1 ;
print hfc --byobs
gnuplot hfc time --time-series --with-lines --output=display
smpl full
</hansl>
A few comments:
* we use djclose in this example so everyone has it.
* gig is an addon, so its "products" are not accessible through "$"
variables. Instead, it uses bundles, so you may fetch them by ordinary
bundle syntax; see the User's Guide and the gig documentation
* when forecasting the variance, you don't want to use the square of the
expectation of e as a predictor of e squared (Jensen's lemma): what you
need is a predictor of e^2. If you use the expectation as your predictor,
that's precisely what h is. As a consequence, in the simple case of the
garch(1,1) model with normal errors, you just forecast h by its past values
(for more complicated models, it's not so easy).
------------------------------**--------------------
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/**servizi/hpp/lucchetti<http://www2.econ.un...
------------------------------**--------------------
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Marta Szymańska -
Riccardo (Jack) Lucchetti