10:59 p.m.
Hello everybody:
One quick question: when estimating a GARCH model (model -> time series -> GARCH),
is it possible to estimate an ARMA model for the equation of the mean? The problem is
that, while lags of the dependent variable and other regressors are easy to include, I
cannot find an option to include the MA part.
Thanks a lot in advanceCheersJavi
8:02 a.m.
On Tue, 27 Feb 2018, Javier García wrote:
Hello everybody:
One quick question: when estimating a GARCH model (model -> time series
-> GARCH), is it possible to estimate an ARMA model for the equation of
the mean? The problem is that, while lags of the dependent variable and
other regressors are easy to include, I cannot find an option to include
the MA part.
No, the natve GARCH command doesn't handle MA() terms in the
conditional mean. However, it's relatively easy to write a script to
estimate that kind of model via conditional QML. For example:
<hansl>
set verbose off
function series llik(series r, matrix param)
series ret = NA
c = param[3]
a = param[4]
b = param[5]
# sanity check
if (c>0) && (a>0) && (b>0) && (a+b<1)
series z = r - param[1]
scalar theta = param[2]
series e2 = filter(z, 1, -theta)^2
series h = c / (1 - a - b)
series h = c + a*e2(-1) + b*h(-1)
ret = -0.5 * (log(2*$pi) + log(h) + e2/h)
endif
return ret
end function
# ---------------------------------------------------
# --- main ------------------------------------------
# ---------------------------------------------------
open djclose
r = 100*ldiff(djclose)
# --- par. initalisation ----------------------------
# MA(1) param via Hannan-Rissanen
ols r 0 r(-1 to -20) --quiet
u = $uhat
ols r 0 u(-1) --quiet
m = $coeff[1]
theta = $coeff[2]
# GARCH params via ordinary garch on HR residuals
u = $uhat
garch 1 1 ; u --quiet --nc
c = $coeff[1]
a = $coeff[2]
b = $coeff[3]
# --- estimation via conditional QMLE --------------
mle l = llik(r, coef)
matrix coef = {m, theta, c, a, b}
params m theta c a b
end mle --robust
</hansl>
Hope this helps.
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
8:50 a.m.
Am 28.02.2018 um 09:02 schrieb Riccardo (Jack) Lucchetti:
On Tue, 27 Feb 2018, Javier García wrote:
> One quick question: when estimating a GARCH model (model ->
time
> series -> GARCH), is it possible to estimate an ARMA model for the
> equation of the mean? The problem is that, while lags of the dependent
> variable and other regressors are easy to include, I cannot find an
> option to include the MA part.
No, the natve GARCH command doesn't handle MA() terms in the conditional
mean.
When you say "native", does that include the gig addon?
cheers,
sven
9:44 a.m.
On Wed, 28 Feb 2018, Sven Schreiber wrote:
Am 28.02.2018 um 09:02 schrieb Riccardo (Jack) Lucchetti:
> On Tue, 27 Feb 2018, Javier García wrote:
>> One quick question: when estimating a GARCH model (model -> time series ->
>> GARCH), is it possible to estimate an ARMA model for the equation of the
>> mean? The problem is that, while lags of the dependent variable and other
>> regressors are easy to include, I cannot find an option to include the MA
>> part.
>
> No, the natve GARCH command doesn't handle MA() terms in the conditional
> mean.
When you say "native", does that include the gig addon?
Yes. In fact I was thinking that adding MA terms to gig may be a nice
project for a student. Hmm...
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
12:23 p.m.
Am 28.02.2018 um 10:44 schrieb Riccardo (Jack) Lucchetti:
On Wed, 28 Feb 2018, Sven Schreiber wrote:
> Am 28.02.2018 um 09:02 schrieb Riccardo (Jack) Lucchetti:
>> On Tue, 27 Feb 2018, Javier García wrote:
>
>>> One quick question: when estimating a GARCH model (model -> time
>>> series -> GARCH), is it possible to estimate an ARMA model for the
>>> equation of the mean? The problem is that, while lags of the
>>> dependent variable and other regressors are easy to include, I
>>> cannot find an option to include the MA part.
>>
>> No, the natve GARCH command doesn't handle MA() terms in the
>> conditional mean.
>
> When you say "native", does that include the gig addon?
Yes. In fact I was thinking that adding MA terms to gig may be a nice
project for a student. Hmm...
Apart from that, could you quickly comment on a two-step estimation
approach like this: First fit an ARMA model to the levels (the mean
equation), then take the estimated residuals and proceed to the GARCH
model of the variance equation.
Of course this wouldn't be an ML estimator, but should be consistent,
no? (If you don't need ARCH-in-mean or something like that.)
cheers,
sven
12:39 p.m.
On Wed, 28 Feb 2018, Sven Schreiber wrote:
Am 28.02.2018 um 10:44 schrieb Riccardo (Jack) Lucchetti:
> On Wed, 28 Feb 2018, Sven Schreiber wrote:
>
>> Am 28.02.2018 um 09:02 schrieb Riccardo (Jack) Lucchetti:
>>> On Tue, 27 Feb 2018, Javier García wrote:
>>
>>>> One quick question: when estimating a GARCH model (model -> time
series
>>>> -> GARCH), is it possible to estimate an ARMA model for the equation
of
>>>> the mean? The problem is that, while lags of the dependent variable and
>>>> other regressors are easy to include, I cannot find an option to include
>>>> the MA part.
>>>
>>> No, the natve GARCH command doesn't handle MA() terms in the conditional
>>> mean.
>>
>> When you say "native", does that include the gig addon?
>
> Yes. In fact I was thinking that adding MA terms to gig may be a nice
> project for a student. Hmm...
Apart from that, could you quickly comment on a two-step estimation approach
like this: First fit an ARMA model to the levels (the mean equation), then
take the estimated residuals and proceed to the GARCH model of the variance
equation.
Of course this wouldn't be an ML estimator, but should be consistent, no? (If
you don't need ARCH-in-mean or something like that.)
Yes, that would be consistent but inefficient. Of course, if you care
about inference you should adjust standard errors somehow. It should be
possible to find an analytical correction, but I suppose nowaday you'd
just bootstrap the whole thing.
-------------------------------------------------------
Riccardo (Jack) Lucchetti
Dipartimento di Scienze Economiche e Sociali (DiSES)
Università Politecnica delle Marche
(formerly known as Università di Ancona)
r.lucchetti(a)univpm.it
http://www2.econ.univpm.it/servizi/hpp/lucchetti
-------------------------------------------------------
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5 comments
3 participants
participants (3)
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Javier García -
Riccardo (Jack) Lucchetti -
Sven Schreiber