Joint Bottom-up Method for Probabilistic Forecasting of Hierarchical Time Series

Many domains involve a hierarchy of time series, where the granular bottom-level series sum to upper-level series based on geography, product category, temporal granularity, or other features. Decision making in these domains requires forecasts that are accurate, probabilistic, and coherent in the sense of respecting the summing structure. In this paper, the authors first show that accurate and coherent probabilistic forecasts for all series in the hierarchy can be obtained by focusing on a joint model of the bottom-level series. Based on this result, the authors devise a Bayesian method that models the bottom-level series jointly, takes into account their contemporaneous and lagged dependence, and outputs a coherent probabilistic forecast of all series in the hierarchy. For empirical validation, the authors compare their method against many state-of-the-art techniques on data on Australian domestic tourism and product sales at Walmart. On each data set, the authors' method outperforms its competition in terms of prediction accuracy. To conclude, the authors demonstrate how our method can support decisions in inventory management of multiple Walmart products.