# Prediction interval for rolling average forecast

In agile software development average of last 3 delivered periods (sprints) is taken to forecast next periods deliverables. I'm not here to discuss if the approach is correct or not. ;)

According to https://otexts.org/fpp2/prediction-intervals.html intervals are calculated as follows:

$$\hat{y}_{T+h|T} \pm c \hat\sigma_h$$

It's easy to calculate $$\hat\sigma_h$$ for one step forecast with rolling average: standard deviation for errors multiplied by multiplier (e.g. 1.96 for 95% interval) assuming normally distributed forecast errors.

How to calculate interval for next steps?