[Gretl-users] ARIMA issues

First of all, kudos to Allin and the development team for making an ARIMA (as opposed to ARMA) routine available in the latest version of gretl! I personally find this of immense utility in my classes as students do not have to back calculate raw level forecasts from differenced data. Now, on the bleaker side, I seem to face some problems with the routine. First of all you may download my test file from http://paravantis.com/cars100.gdt (It represents the number of cars per 100 people in Greece from 1970 to 2003.) The data set includes 3 columns: Cars100 (cars per 100 people), DIFF1_Ca (1st differences) and DIFF2_Ca (2nd differences). Now, in the past Allin indicated to me that he felt that taking the 2nd differences of Cars100 was probably OVERDIFFERENCING. Yet, using correlograms and taking into account which of these series has the SMALLEST STANDARD DEVIATION, I think that the second differences are "best" (and it is kept in mind that mild underdifferencing may be corrected with more AuroRegressive terms while mild overdifferencing may be corrected with more Moving Average terms). Coming now to the crunch of the matter, there appear to exist QUITE A FEW ARIMA models that CANNOT be estimated with gretl which gives a dialog box stating "The convergence criterion was not met". UNFORTUNATELY, there is NO OPTION to increase the number of iterations (or make the convergence threshold more lax). These models include: ARIMA(1,2,1) ARIMA(0,2,1) It should be noted that these models MAY BE ESTIMATED with X-12_ARIMA but not with the "default" ARIMA routine. Here is what I would appreciate having as feedback from the respected gretl community: 1. How do you stand on the differencing issue? Do you side with 1st or 2nd differences? Does it really matter since we can "correct" by including more AR or MA terms? 2. What causes the problem with the default ARIMA routine? Is it "safe" to use X-12-ARIMA in all cases (even with unseasonal data)? Thanking you all for you time, John Paravantis University of Piraeus Greeece