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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?

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  • $\begingroup$ Sounds like a good case for running a vector auto regression (VAR)? Loosely, you're doing the same thing as in an AR model but with vectors. You can extend to the full vectorized version of ARIMA as well. $\endgroup$ – Matthew Gunn Jun 9 '16 at 18:38
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You are asking about hierarchical forecasting. The two approaches you describe are known as "top-down" and "bottom-up" forecasting.

I personally have usually found combining both approaches to yield better forecasts - on all levels of the hierarchy.

This section in this extremely good online forecasting textbook describes the different ways to do hierarchical forecasting, with an emphasis on this "optimal combination" approach. The hts package for R implements it.

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I would recommend the following very good article on forecasting aggregated time series, it should answer your questions and provide useful references on the topic: Lütkepohl (2010): Forecasting Aggregated Time Series Variables - A Survey. OECD Journal: Journal of Business Cycle Measurement and Analysis, 3(2):1-26.

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