fiddle with the convergence criterios (# of iterations) on the ARMA dialog box! [ ... ] responsible for the non-convergence in your first model. the option of using X-12-ARIMA for ARMA estimation, and in this case it will produce estimates for you. The issue we have here is very similar to the GARCH case that was discussed here about 3 weeks ago (see http://ricardo.ecn.wfu.edu/pipermail/gretl-users/2006-January/000292.html). The "ARMA(1,1)--no constant" model has a likelihood function that, with this dataset, appears to have no maximum inside the admissible parameter region. I tried the same model with several packages: all of them report problems. For example, R's "tseries" package yields Coefficients: ar1 ma1 intercept 0.6318 -1.0000 0.0440 s.e. 0.1522 0.1102 0.0129 And clearly the idea here is to stop when the algorithm takes you to a noninvertible MA structure. Ox arfima package gives: Coefficient Std.Error t-value t-prob AR-1 0.648324 0.1489 4.36 0.000 MA-1 -1.000000 0.1365 -7.32 0.000 which is very close to R. Eviews (ugh!) gives AR(1) 0.460374 0.643653 0.715253 0.4804 MA(1) -0.674092 0.551803 -1.221617 0.2320 which is rather strange, considering that the score vector at that point is not zero (but Eviews in not renowned for its numerical strength). What *we* do here is simply give up. Actually, those who use linux will perhaps see the message MA root 0 = 0.999999 arma: MA estimate(s) out of bounds bhhh_max: crit = 8.44786e-06, tol = 1e-06, err = 40 arma: bhhh_max returned 40 but that is issued to stderr, not to the main output (Allin, maybe we ought to redirect this?) As Ricardo pointed out, the trouble here is probably overdifferencing, which induces a unit root in the MA part. If you try working with 1st differences instead things are much much better. Try this: genr ccars = cum(cars) arma 1 1 ; ccars Model 5: ARMA estimates using the 30 observations 1971-2000 Dependent variable: ccars VARIABLE COEFFICIENT STDERROR T STAT P-VALUE const 0.123980 0.139820 0.887 0.38279 ccars(-1) 0.863621 0.230057 3.754 0.00081 *** e(-1) -0.0827397 0.400739 -0.206 0.83792 If you get an adequate ARMA representation for "ccars", obviously any ARMA representation for "cars" contains a unit root in the MA part, due to excessive differencing. Hence the numerical problems. -- Riccardo "Jack" Lucchetti Dipartimento di Economia Facoltà di Economia "G. Fuà" Ancona