# ARIMA - Forecasting - Future Errors?

I have a question regarding forecasting with my ARIMA model. Let's say we have found ARIMA(1,1,1) as the best model based on AIC or BIC.

Now, if I want to estimate the value of (t+1) I can substitute in the equation the values of y(0) and e(0). Ok, so I would like to predice now for the horizon t=2. What can I do with the value of e(1) if it is in the future, thus, I don't know the real value and I cannot calculate the error!?

I would say there must be a way to also estimate the error (based on expectancies) or make future errors 0, but then my MA part is completely useless right?

To get the expected value of $y_{t+2}$, you will need to plug in the expected value of $\epsilon_{t+1}$. Which is zero, since ARIMA assumes normally distributed innovations with mean zero.
Plus, your third paragraph already hints at an extension: if you are not only interested in point forecasts (where your criticism applies), but also in predictive densities or prediction intervals, then the full density of $\epsilon_{t+1}$ does indeed come in, and depending on your MA parameter estimates may have quite some effect, indeed.