Lets say I have two time series a and b and I predict the next value and a prediction interval (say lower and upper 80%) of each of these two. I end up with something like that: a: [10, 20, 30] and b: [2, 7, 12] (as [lo80%, prediction, high80%]). As these time series are independent, I see I could just add 20 + 7 to get a prediction of a + b, but what about the prediction interval? I suppose I cant just add them to [12, 27, 42], right?
(Sorry if it is too simple a question)