# How to calculate forecast error (confidence intervals) for ongoing periods?

I often need to forecast for future periods in monthly series of data.

Formulas are available to calculate the confidence interval at alpha for the next period in the time series, but this never includes how to treat the second period, and third, etc.

I’d visually imagine that if any forecast was graphed with upper and lower confidence intervals, generally those intervals should exponentially increase or decrease against the mean forecast, as uncertainty is a cumulative force.

Let’s say I had unit sale of
Apr = 10 May = 8 June = 11 July = 13
and no other context such as seasonality or population data

We need to forecast (albeit blindly) August, September, October.

What method would you use?
and more importantly here, how will you measure confidence for September and October?

Sorry that this might be a simple question for some experts – I have been digging far for a clear answer, and I’m sure this is something all amateurs like me would love to understand.

• since you have a short forecasting interval you may try to forecast by exponential smoothing (in R it is the `ets()` function from `forecast`)
• another option would be to model it like ARIMA process (the same library has `auto.arima()`)