[Gretl-users] ARIMA(0,0,1)(0,0,1) forecasts

Hi everyone, I'm having trouble understanding the way that Gretl computes forecasts for ARIMA(0,0,1)(0,0,1) models. If I generate a random data set and fit this model (using either algorithm) to get the estimates theta_1 and Theta_1, and then generate a forecast, then I would expect the forecast to be computed using the polynomial 1 + theta_1*L + Theta_1*L^4 + theta_1*Theta_1*L^5 p.176 of the manual appears to suggest that this should be the case. However, if I copy the estimates and residuals to a spreadsheet and calculate the same forecast 'manually' I get a different result. Furthermore, after a little experimenting, I have found that if I use the polynomial 1 + theta_1*L + Theta_1*L^4 - theta_1*Theta_1*L^5 I get exactly the same forecast as Gretl. However, I can't see how this can be correct. In particular, this polynomial cannot be written as the product of two factors, which means that it can't be a ARIMA(0,0,1)(0,0,1) model (can it?). What am I missing here? Thanks in advance for any help. Chris.