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@univpm.it>`

On Fri, 9 Nov 2012, Marta Szymańska wrote:This should be intended as a reply to Tomasz too.

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.

Here's a variation on your script that should work as intended:

<hansl>

include gig.gfn

open djclose.gdt

RETURN = ldiff(djclose)series e = model["uhat"]

model = gig_setup(RETURN,1,const)

gig_set_dist(&model, 2)

gig_estimate(&model)

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@univpm.it

http://www2.econ.univpm.it/servizi/hpp/lucchetti

--------------------------------------------------

_______________________________________________

Gretl-users mailing list

Gretl-users@lists.wfu.edu

http://lists.wfu.edu/mailman/listinfo/gretl-users