Say I am forecasting sales for a company that has four regions using ARIMA models. Each region behaves a little differently so four different ARIMA models are used. In order to forecast overall sales for the company would it be better to build a new model or could I just add all of the forecasts for the four regions together?
My instinct says that adding the forecasts would be more accurate as some of the features of the data could be lost when aggregated at a company level but I wasn't sure how statistically sound that methodology was. Also, would it be acceptable to add the 80%/95% prediction intervals as well to come up with overall prediction intervals?