> 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.) > I think you have few observations to work with standard time series tecniques. In ARIMA models you do not have unbiadness in the estimators, you only have consistency, and this is a property that justifies good estimations only with a large number of observations. The sample correlograms are only consistent as well, so you may not trust in them with so few observations. Few observations produces large standard deviations of the coefficients so the estimations have a large variance (they are very inaccurate) and all the tests tend to be not rejected. > 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 think the problem here is that you have so few observations and the variance of the coefficient estimator is so large that the change in the estimations from one iteration to the following is so large that gretl cannot converge. I asked in a previous message to this list to have a method for changing the number of iterations. You may read the response in http://ricardo.ecn.wfu.edu/pipermail/gretl-users/2006-February/000499.html but I think probably this will not work in your case. > 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? > Apart form the graphics (and with your graphic I would vote for I(2)), we normally use a test (as ADF: in /variable/augmented Dickey-Fuller test) but with your data you will see that all the tests are not rejected, and this is only because your data have no enough information. > 2. What causes the problem with the default ARIMA routine? > Too few observations. > Is it "safe" > to use X-12-ARIMA in all cases (even with unseasonal data)? > No. In some cases you may obtain an estimation, but in your case you may not trust in it because you have a very large variance.