Okay, I think I understand AR models correctly for forcasting. The value of a time series S at t+1 is predicted by S(t+1) = a1*S(t) + a2*S(t-1) + a3*S(t-2) + ....... where the an's are some parameters.As I understand it, a MA forcasting model would have the same basic form, but with the 'error terms' replacing the known S's, so S(t+1) = a1*e(t) + a2*e(t-1) + a3*e(t-2)+... However I can't find anything that says exactly what the error terms are. Are they simply the deviation from the moving average?And an ARMA forcasting model would simply have the form S(t+1) = a1*S(t) +...+ an*S(t-n) + b1*e(t) +...+ bn*e(t-n) ?Thanks for any help!

Hamilton, Time Series Analysis, Chapter 3.M.

Okay, I got that book. I'm trying to come up with an ARMA(1,1) forecaster to predict 1 timestep ahead.An ARMA(1,1) model for a time series e with 0 mean is[1] Y(t)=(1 + theta*L)/(1 - phi*L)*e(t)L is the lag operatorThe book gives this equation for an ARMA(1,1) 1 step ahead forcaster[2] Y(t+1)=(phi+theta)/(1+theta*L)*Y(t)However, since we know the time series e, can't we just combine the two equations to get the following [3] ?[3] Y(t+1)=(phi+theta)/(1-phi*L)*e(t)Is that right?