Hierarchical Industrial Demand Forecasting with Temporal and Uncertainty Explanations

Hierarchical time-series forecasting is essential for demand prediction across various industries. While machine learning models have obtained significant accuracy and scalability on such forecasting tasks, the interpretability of their predictions, informed by application, is still largely unexplored. To bridge this gap, we introduce a novel interpretability method for large hierarchical probabilistic time-series forecasting, adapting generic interpretability techniques while addressing challenges associated with hierarchical structures and uncertainty. Our approach offers valuable interpretative insights in response to real-world industrial supply chain scenarios, including 1) the significance of various time-series within the hierarchy and external variables at specific time points, 2) the impact of different variables on forecast uncertainty, and 3) explanations for forecast changes in response to modifications in the training dataset. To evaluate the explainability method, we generate semi-synthetic datasets based on real-world scenarios of explaining hierarchical demands for over ten thousand products at a large chemical company. The experiments showed that our explainability method successfully explained state-of-the-art industrial forecasting methods with significantly higher explainability accuracy. Furthermore, we provide multiple real-world case studies that show the efficacy of our approach in identifying important patterns and explanations that help stakeholders better understand the forecasts. Additionally, our method facilitates the identification of key drivers behind forecasted demand, enabling more informed decision-making and strategic planning. Our approach helps build trust and confidence among users, ultimately leading to better adoption and utilization of hierarchical forecasting models in practice.

💡 Research Summary

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The paper tackles the pressing need for interpretability in large‑scale hierarchical probabilistic time‑series forecasting (HTSF), a cornerstone of industrial demand planning. While deep‑learning models have dramatically improved forecast accuracy and scalability, their black‑box nature hampers trust and actionable insight for stakeholders who routinely ask three questions: (RQ1) which variables drive the forecast, (RQ2) which historical time steps are most influential, and (RQ3) why forecasts shift when input data change. Existing interpretability techniques for time‑series either ignore hierarchical relationships, cannot handle probabilistic outputs, or become computationally infeasible when the hierarchy contains thousands of series.

To bridge this gap, the authors propose two complementary adaptations that enable a wide range of post‑hoc explanation methods to work with hierarchical probabilistic models. First, subtree approximation decomposes the global importance computation into a set of adjacent subtrees. By restricting importance calculations to each subtree and then aggregating the results, the method preserves hierarchical coherence while reducing the computational complexity from quadratic in the number of series to near‑linear. This makes it feasible to compute variable‑ and time‑step‑level contributions even for hierarchies with more than ten thousand nodes.

Second, the authors introduce a quantile‑based deterministic alternative for probabilistic forecasts. Instead of trying to explain an entire distribution, they extract a small set of quantiles (e.g., 10 %, 50 %, 90 %) from the predicted distribution and treat these quantiles as deterministic outputs. This transformation allows gradient‑based, perturbation‑based, or surrogate‑model‑based explainability methods to be applied unchanged, while still capturing essential aspects of forecast uncertainty. The quantiles themselves become interpretable objects, enabling analysts to see why prediction intervals widen or narrow under different conditions.

Because public time‑series datasets lack ground‑truth explanations, the authors construct a semi‑synthetic benchmark that blends real Dow Chemical demand data with synthetically injected anomalies and dependency patterns at various hierarchy levels. Each injected pattern is labeled with its true explanatory factors, providing a reliable testbed for evaluating explanation quality. Experiments on this benchmark show that subtree approximation improves overall variable‑importance accuracy by an average of 62 % and target‑only importance by 12 %. In the probabilistic setting, the combined approach yields a 10‑25 % boost in explanation fidelity over baseline methods, while also cutting runtime by a factor of three.

Beyond synthetic tests, the paper presents three real‑world case studies. In the first, the method identifies a small group of products that disproportionately affect aggregate demand, allowing planners to focus inventory controls. The second case examines the COVID‑19 pandemic’s impact: the explanation reveals a shift in the temporal relevance of recent sales versus longer‑term trends, and it quantifies the increase in forecast uncertainty during the disruption. The third case links fluctuations in raw‑material prices to widening prediction intervals, giving procurement teams a clear signal to hedge price risk. Domain experts from Dow Chemical confirmed that these insights were directly actionable and increased confidence in the forecasting system.

In summary, the contribution consists of (1) a generalized framework for adapting existing interpretability techniques to hierarchical and probabilistic forecasting, (2) a novel benchmark for quantitative evaluation of explanations in HTSF, (3) empirical evidence of substantial accuracy and efficiency gains, and (4) demonstrable real‑world utility in industrial demand planning. The authors suggest future work on automated subtree selection, richer quantile ensembles for uncertainty decomposition, and online explanation generation for streaming data. This research paves the way for trustworthy, transparent demand forecasting systems that can be confidently deployed at enterprise scale.