I'm using ARIMA models to estimate sales forecast for a company. The company's sales channel is broken down into 4 sales channels and I'm running 4 different models to estimate the sales for each channel. Eventually, I'm going to aggregate the sales of these channels to find the total forecasted sales for the whole company. My questions is, how should i go about finding the confidence interval for the overall forecast? Adding up the confidence intervals of each channel is not correct since that will give me a very large interval.
I'd really appreciate if anyone can give me some idea on how to approach this sort of issue. Thanks in advance!