# Using ARMA model for future forecasting

I just started learning about times-series modeling and I'm confused by the following scenario:

Let's assume we train a ARMA(p, q) model on a time-series $\{x_1, x_2, ..., x_t\}$.

Later in a test set, which starts at time $t+d$ with $d>max(p,q)$ we want to predict the future value $x_{t+d+1}$, given the history $\{x_{t + d - p}, ..., x_{t+d}\}$. How can we obtain the values $\{\epsilon_{t + d - q}, ..., \epsilon_{t+d}\}$?

Do we set the $\epsilon$-values to zero? If yes, what is the advantage of ARMA(p, q) over AR(p) in this case?