Re: [Gretl-devel] ARMAX and diffs

On Tue, 6 May 2008, Ignacio Diaz-Emparanza wrote: ... Ignacio, after some pondering, I believe you're right. What I would consider a proper fix for this issue, however, takes us right in the middle of the parallel discussion about backward-incompatible changes. Let me explain. To recap briefly what's in the manual already, what we currently have under the "arima" heading is in fact a pair of quite different things. On one hand, we have that ML estimation (carried out via the Kalman filter) estimates a model like (1) A(L) (y_t - x_t'\beta) = C(L) e_t If we believe that the differencing operator is part and parcel of the A(L) polynomial, we ought to difference x_t as well, not just y_t (contrary to what we do now). This would be, in itself, a backward-incompatible change already. Now consider the class of models that we handle via conditional ML: here we have (2) A(L) y_t = x_t'\beta + C(L) e_t. As the manual says, whenever x_t includes anything more than the constant, (1) and (2) are fundamentally different models, since the term x_t'\beta can be considered as the conditional mean of y_t with respect to two different information set. In the context of (2), the A(L) polynomial does _not_ apply to x_t, so there's no reason to difference x_t too. The important thing here is that (1) is the formulation generally adopted in the time-series literature, while (2) resembles more the models econometricians use, (ARDL models, GARCH models, and so on). If we implement the change proposed by Ignacio (which, I repeat, makes perfect sense for (1)), the two models would diverge in their behaviour and interpretation even more, to the point that I wouldn't find it inconceivable to have two separate commands and two different GUI menu entries for (1) and (2) (although, it must be said, it'd be relatively easy to estimate (1) via conditional ML if we wanted to). Opinions? Riccardo (Jack) Lucchetti Dipartimento di Economia Università Politecnica delle Marche r.lucchetti(a)univpm.it http://www.econ.univpm.it/lucchetti