Abstract:
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An important task for any large-scale business is to prepare forecasts of business metrics, such as revenue, cost, and event occurrences, at different time horizons. Often these businesses are structured in a hierarchical manner by line of business, division, geography or a combination thereof. Projections for these business metrics may have been obtained independently, and there is no guarantee that forecasts are aggregate consistent according to the hierarchical structure, while remaining as accurate as possible. Also, it is often important to achieve accurate forecasts at certain levels of the hierarchy. We propose a Bayesian hierarchical method that treats the "base" forecasts (those initially provided) as observed data, which are then updated and obey the hierarchical organizational structure. In addition, by leveraging the prior covariance matrix, we set up a heterogeneous loss function to obtain higher accuracy at the levels prescribed by the user. We develop a novel approach to hierarchical forecasting that provides an organization with optimal forecasts that reflect their preferred levels of accuracy while maintaining the proper additive structure of the business.
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