[Gretl-users] Tranfer function models

[Ignacio Diaz-Emparanza]

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
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