Re: [Gretl-users] Out-of-sample forecasting

[Marta Szymańska]

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.univpm.it/servizi/hpp/lucchetti>
> ------------------------------**--------------------
> _______________________________________________
> Gretl-users mailing list
> Gretl-users(a)lists.wfu.edu
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>

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.lucche...@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.lucche...@univpm.it
 http://www2.econ.univpm.it/servizi/hpp/lucchetti
--------------------------------------------------
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