GMP-AR: Granularity Message Passing and Adaptive Reconciliation for Temporal Hierarchy Forecasting

TL;DR

This work tackles coherent forecasting across multiple temporal granularities in temporal HTS. It introduces GMP-AR, a framework that combines Granularity Message Passing with Adaptive Reconciliation to improve forecast accuracy while preserving coherence, augmented by a task-based optimization module for real-world constraints. Empirical results on Electricity, Traffic, and Exchange Rate datasets, plus a real Alipay deployment, show consistent gains over state-of-the-art baselines and validate the effectiveness of the component ablations. The approach enables practical, constraint-aware forecasting in large-scale, real-world systems like payment traffic management, with strong potential for broader adoption in operational settings.

Abstract

Time series forecasts of different temporal granularity are widely used in real-world applications, e.g., sales prediction in days and weeks for making different inventory plans. However, these tasks are usually solved separately without ensuring coherence, which is crucial for aligning downstream decisions. Previous works mainly focus on ensuring coherence with some straightforward methods, e.g., aggregation from the forecasts of fine granularity to the coarse ones, and allocation from the coarse granularity to the fine ones. These methods merely take the temporal hierarchical structure to maintain coherence without improving the forecasting accuracy. In this paper, we propose a novel granularity message-passing mechanism (GMP) that leverages temporal hierarchy information to improve forecasting performance and also utilizes an adaptive reconciliation (AR) strategy to maintain coherence without performance loss. Furthermore, we introduce an optimization module to achieve task-based targets while adhering to more real-world constraints. Experiments on real-world datasets demonstrate that our framework (GMP-AR) achieves superior performances on temporal hierarchical forecasting tasks compared to state-of-the-art methods. In addition, our framework has been successfully applied to a real-world task of payment traffic management in Alipay by integrating with the task-based optimization module.

Figures (8)

• Figure 1: An example of temporal hierarchical time series (HTS) structure for ten-minute frequency as the bottom level, half-hour and hour frequencies as aggregated levels of coarser granularity.
• Figure 2: The notation of each node in Fig. \ref{['fig:temporal_hts']} observed at timestamp $t = 6$ and $\tau = 1$.
• Figure 3: The architecture of GMP-AR: the red dashed box is the granularity message passing component including the granularity input transformation module, temporal feature extractor and two granularity feature fusion modules. This component generates the representation of nodes used to generate base forecasts and adaptive weights. The light green dashed box is the reconciliation module that produces the final results, including the adaptive reconciliation module for forecasting tasks and task-based optimization module to adapt to general real-world tasks.
• Figure 4: The process of granularity input transformation: the orange cycle is the top-down proportion transformation module that produces the disaggregation proportions for child nodes, the red rectangle is the child distribution modeling module which extracts valid information of finer granularity for parent nodes; the blue box concatenate these processed inputs with normalized value and put them into temporal feature extractor to extract dynamic patterns.
• Figure 5: The temporal hierarchical structure of mobile payment service of Alipay, with weekly traffic forecast as the root node, daily forecast as the second level, and hourly forecast as leaf nodes ($N_3 = \{1, 7, 168\}).$