> 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. > > I do not know what models yo got estimated, I only know that the models you sent in your previous message was not working. I suppose you may have success with models such as ARMA(1,2,0) or ARMA(2,2,0), this models are linear, so maximum likelihood has an analitical solution and it is equivalent to OLS. So in this case you obtain a direct estimation. The models with a MA part (and the ARxARs as well) are not linear and finding the maximum of the likelihood function require an iterative optimization routine. The difference between the estimated likelihood from one iteration to the following one may be large if you have few data, and so the process is difficult to converge.