On Tue, 2 Nov 2010, [iso-8859-1] G�staf Steingr�msson wrote: Also you are not subscribed to the gretl-devel list under the email address you're using, which may explain communication difficulties. The first point is that when gretl estimates an ARMA model with mean term \mu via exact ML, the model is in fact \phi(L) (y - \mu) = \theta(L) e_t This is explained in the Gretl User's Guide, chapter 21 (see equations (21.4) and (21.5) in particular. This means that in your forecasting equation you need to replace c with (1 - \phi)c on the right-hand side. This will produce forecast values that are close to those given by gretl. But they will not be identical, for this reason: what gretl produces as the ARMA residual, available via the accessor $uhat, is the one-step ahead forecast error, y_t - E_{t-1} y_t where E_{t-1} y_t is the optimal forecast of y_t as of date t-1, produced by the Kalman filter. Now the point is that this value is not exactly the one that is needed for "e(t-1)" in the forecasting equation you cite. To make that equation valid you need the optimal estimate of the (t-1)-dated innovation based on all information up to t - 1. This is implicitly produced by the Kalman filter, but it is not the same as gretl's reported $uhat. The difference arises because observation of y at t allows revision of the optimal estimates of the underlying innovations at t-1 and t. For example, consider a Gaussian ARMA(1,1) process with an unconditional mean of zero. Let the first observation, y_1, equal 1.5. Then the first forecast error ($uhat[1]) is also 1.5. But this does not mean that the optimal estimate of e_1 is 1.5, once y_1 is observed. Rather, the positive value of y_1 suggests that the pre-sample value e_0 was positive, and the optimal estimate of e_1 (which we need for forecasting y_2) will be < 1.5. Allin Cottrell