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 www.et.bs.ehu.es