Re: [Gretl-users] Tranfer function models
El Wednesday 13 February 2008 10:39:27 Riccardo (Jack) Lucchetti escribió:
On Wed, 13 Feb 2008, Nieves Sánchez Martínez wrote:
> Hello,
> I need something like
>
> y_t = (B(L)/A(L)) x_t + (C(L)/A'(L)) u_t
>
> where L is the lag operator and u_t is a white noise sequence and A(L)
> and A'(L) are different. I think --conditional option doesn't do that
> and in the manual I haven't found it. Is it possible?
Short answer: yes and no :-)
Long answer: what arma --conditional can handle is the special case
A(L) = A'(L). What you can do is write a script that estimates the general
case, perhaps via MLE, or via the multi-stage approach described in
Brockwell & Davis. All the tools you need are in gretl already, but you
don't get a pre-cooked estimator, you have to write it yourself. One of
the things we are considering for the next release, or possible the one
after, is a user-level implementation of the Kalman filter, which should
make this task (relatively) painless.
You may do also an estimation of an unrestricted version of your model.
Multiplying your equation by AA(L)=A(L)*A'(L) and defining B'(L)=A'(L)*B(L)
and C'(L)=A(L)*B(L) you will have
AA(L)y_t = B'(L) x_t + C'(L) u_t
which is estimable in gretl because has the structure that Jack mentioned.
Note that if A(L) has order "a" , A'(L) order a', B(L) order
"b" and C(L)
order "c", AA(L) will be of order a+a', B'(L) will be of order a'+b
and C'(L)
will be of order a+b.
In some cases this may be not appropiate for your model, but at least can help
in identifying the orders of B(L) and A(L) and you can obtain a forecast
based on this model.
--
Ignacio Diaz-Emparanza
DEPARTAMENTO DE ECONOMÍA APLICADA III (ECONOMETRÍA Y ESTADÍSTICA)
UPV/EHU
Avda. Lehendakari Aguirre, 83 | 48015 BILBAO
T.: +34 946013732 | F.: +34 946013754
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