[Gretl-devel] ARIMA news

Hello all, Ignacio, Jack and I have had a conversation lately about ARIMA estimation in gretl. The outcome is that various problems have been fixed, but also that I've introduced a backward-incompatible change in CVS which I'd like to expose, and on which I'd appreciate any comments. (And I'd particularly appreciate if Ignacio or Jack could correct anything erroneous below!) The backward-incompatible change concerns ARIMAX models -- that is, ARIMA models including exogenous regressors -- but we can get at it by starting from the most basic ARMA specification: \phi(L) y_t = \theta(L) \epsilon_t where \phi(L) and \theta(L) are polynomials in the lag operator, L, and \epsilon is a white-noise process. The first question is: how do we handle the situation where the level of y_t is a function of some exogenous variable(s), X_t? There are two options: Model A: \phi(L) y_t = X_t\beta + \theta(L) \epsilon_t Model B: \phi(L) (y_t - X_t\beta) = \theta(L) \epsilon_t Model A might be described as an ARMA model augmented with exogenous variables, while B might be described as a regression model with ARMA errors. This choice is discussed in the Gretl User's Guide. (Short story: we do Model B if exact ML is chosen, and Model A if conditional ML is chosen; except that we do Model B regardless, if estimation via X-12-ARIMA is selected). The new issue, however, is how we handle a non-zero integration order (the 'I' in ARIMA). Take the simplest case: non-seasonal order 1, seasonal order 0. If we're doing exact ML, and hence have effectively chosen B above, the options are: Model C: \phi(L) ((1-L) y_t - X_t\beta) = \theta(L) \epsilon_t Model D: \phi(L) (1-L) (y_t - X_t\beta) = \theta(L) \epsilon_t In practical terms the issue between C and D is, given that we're differencing y_t, do we also difference X_t? (No = C, Yes = D.) Up till now we have been doing C, and there's nothing inherently wrong with that, but for the sake of compatibility with most other ARIMA software we should be doing D. And in current CVS we do D, unless the new option -y (or --y-diff-only) is given in conjunction with the arima command, in which case C is restored. I don't know how many gretl users are estimating ARIMAX models, but obviously if anyone is doing so, we'd like to hear what they have to say. Allin.