DeepHGNN: Study of Graph Neural Network based Forecasting Methods for Hierarchically Related Multivariate Time Series

TL;DR

DeepHGNN tackles forecasting for hierarchically related multivariate time series by introducing a two-block end-to-end graph-based framework. It combines a Multivariate Graph Model (MGM) to capture spatio-temporal dependencies with a Hierarchical Aggregation Block that reconciles bottom-level forecasts up the hierarchy using a summing matrix $S$ and a hierarchical loss, while allowing the adjacency $A$ to adapt to changes in structure. By sharing signals across hierarchy levels and leveraging hierarchical interpolation, it improves forecast accuracy and coherence, outperforming baselines and state-of-the-art end-to-end methods on Favorita, M5, and Australian Tourism datasets. The work advances graph-based hierarchical forecasting and highlights practical gains, though it notes scalability as a key challenge for very large hierarchies and dynamic structures.

Abstract

Graph Neural Networks (GNN) have gained significant traction in the forecasting domain, especially for their capacity to simultaneously account for intra-series temporal correlations and inter-series relationships. This paper introduces a novel Hierarchical GNN (DeepHGNN) framework, explicitly designed for forecasting in complex hierarchical structures. The uniqueness of DeepHGNN lies in its innovative graph-based hierarchical interpolation and an end-to-end reconciliation mechanism. This approach ensures forecast accuracy and coherence across various hierarchical levels while sharing signals across them, addressing a key challenge in hierarchical forecasting. A critical insight in hierarchical time series is the variance in forecastability across levels, with upper levels typically presenting more predictable components. DeepHGNN capitalizes on this insight by pooling and leveraging knowledge from all hierarchy levels, thereby enhancing the overall forecast accuracy. Our comprehensive evaluation set against several state-of-the-art models confirm the superior performance of DeepHGNN. This research not only demonstrates DeepHGNN's effectiveness in achieving significantly improved forecast accuracy but also contributes to the understanding of graph-based methods in hierarchical time series forecasting.

Figures (4)

• Figure 1: Hierarchical data represented in the form of a graph.
• Figure 2: DeepHGNN Framework
• Figure 3: Hierarchical Information propagation (The arrows represent information flow and dotted lines represent hierarchical connection)
• Figure 4: The critical difference diagram shows the mean ranks of each model evaluated.