I've been using gretl for different kinds of models and I have a question about the ARIMA models. I use the graphic interface and not the console, because I haven't had time to learn the commands. After calculating the models with several lags on the dependent variable I attempted to use the parameters to replicate the fitted values using Excel. My question is how the fitted values are calculated, because I don't know how the first values are calculated, since there is no data for the lagged variable. 

I figured that if, for example, the model I calculated uses the third and fourth lag of the dependent variable, then the first and second fitted values set the third and fourth lag to be equal to zero, so that the parameter for the third and fourth lag is not used. But what happens at the third fitted value? 

Thank you for your help and for this great program. Please let me know if you need any more information. 

Regards,

Thomas Wagner