# Sampling from forecasting interval

Suppose I have an ARIMA model with $n$ step ahead forecasts and forecast intervals. If I want to sample from those forecasts:

• One way to look at is: take one observation from the prediction distribution in each step, then you have one path. Repeat this process.

• But when you choose your first observation from the first prediction distribution, the second observation is dependent on the first one, isn't it?

Any insights?

• Yes, you are right. And of course we want this dependence. If your time series were independent, there would not be a point to time series modeling. Does this answer your question, or could you clarify if something is still unclear to you? – Stephan Kolassa Nov 1 '17 at 7:28
• What is the exact question here? Also note that ARIMA is an acronym, so we do not use formula formatting for it, we just use capital letters. – Richard Hardy Nov 1 '17 at 11:03
• @StephanKolassa, yes it does. It seems that simulate function in forecast package in R does the job for sampling from the forecasts. This link is useful. – soheil Nov 1 '17 at 14:15