Hermes: A Multi-Scale Spatial-Temporal Hypergraph Network for Stock Time Series Forecasting

Time series forecasting occurs in a range of financial applications providing essential decision-making support to investors, regulatory institutions, and analysts. Unlike multivariate time series from other domains, stock time series exhibit industry correlation. Exploiting this kind of correlation can improve forecasting accuracy. However, existing methods based on hypergraphs can only capture industry correlation relatively superficially. These methods face two key limitations: they do not fully consider inter-industry lead-lag interactions, and they do not model multi-scale information within and among industries. This study proposes the Hermes framework for stock time series forecasting that aims to improve the exploitation of industry correlation by addressing these limitations. The framework integrates moving aggregation and multi-scale fusion modules in a hypergraph network. Specifically, to more flexibly capture the lead-lag relationships among industries, Hermes proposes a hyperedge-based moving aggregation module. This module incorporates a sliding window and utilizes dynamic temporal aggregation operations to consider lead-lag dependencies among industries. Additionally, to effectively model multi-scale information, Hermes employs cross-scale, edge-to-edge message passing to integrate information from different scales while maintaining the consistency of each scale. Experimental results on multiple real-world stock datasets show that Hermes outperforms existing state-of-the-art methods.

💡 Research Summary

The paper introduces Hermes, a novel stock time series forecasting (STSF) framework that explicitly models both inter‑industry lead‑lag relationships and multi‑scale temporal dynamics using a spatial‑temporal hypergraph network. Traditional approaches either treat each stock independently or rely on simple graph structures that can only capture pairwise interactions, thereby ignoring higher‑order industry correlations and the temporal precedence that often exists between sectors (e.g., technology innovations leading energy sector performance). Existing hypergraph‑based methods improve intra‑industry modeling by grouping stocks of the same industry into hyperedges, yet they fall short in two critical aspects: (1) they do not adequately capture dynamic lead‑lag effects across industries, and (2) they operate on a single temporal resolution, missing valuable information present at different granularities (fine‑grained periodic patterns versus coarse‑grained trends).

Hermes addresses these gaps through two key modules integrated into a unified architecture:

1. Hyperedge‑Based Moving Aggregation (MA) Module

   • A sliding window mechanism partitions the historical series into overlapping temporal segments.
   • Within each window, stocks belonging to the same industry are aggregated via their hyperedge, producing a condensed representation that respects industry membership.
   • Dynamic temporal aggregation is performed using a learnable Markov‑distance similarity matrix, yielding a time‑varying adjacency matrix that reflects how the influence of one industry evolves and potentially leads or lags another.
   • This design enables the network to learn directed, time‑dependent inter‑industry interactions rather than static, symmetric connections.

2. Multi‑Scale Fusion (MSF) Module

   • The raw multivariate series (X \in \mathbb{R}^{N \times T \times F}) is down‑sampled into (S) different scales via 1‑D convolutional layers with varying kernel sizes and strides, producing scale‑specific sequences (X_i).
   • Each scale undergoes a Causal‑Mixing transformation: a series of per‑time‑step MLPs that enforce causality (future steps cannot influence past representations) while enriching the feature space.
   • For each scale, a hypergraph is constructed where hyperedges correspond to industry groups.
   • Cross‑scale edge‑to‑edge message passing is then executed: hyperedges from different scales exchange information based on learned similarity scores, preserving the internal consistency of each scale while allowing fine‑grained periodic signals and coarse‑grained trend cues to mutually inform each other.

The overall pipeline proceeds as follows: (i) multi‑scale decomposition and causal mixing, (ii) construction of scale‑specific hypergraphs, (iii) application of the moving aggregation module to capture lead‑lag dynamics, (iv) cross‑scale fusion via edge‑to‑edge messaging, and (v) a final MLP predictor that outputs next‑day closing prices or return ratios.

Empirical evaluation is conducted on several real‑world datasets, including Chinese A‑share markets and major US indices. Hermes is benchmarked against state‑of‑the‑art baselines such as Transformer‑based time‑series models, graph neural networks (GNNs), and prior hypergraph models (e.g., THGNN, ESTIMATE). Across metrics—Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and directional accuracy—Hermes consistently outperforms competitors, achieving improvements ranging from 5% to 12% on average. Ablation studies confirm that both the moving aggregation and multi‑scale fusion components contribute significantly to performance gains; removing either leads to noticeable degradation. Sensitivity analyses on window size and the number of scales demonstrate robustness of the design.

In conclusion, Hermes demonstrates that enriching hypergraph representations with dynamic temporal aggregation and multi‑scale cross‑hyperedge communication can capture complex market mechanisms that static or single‑scale models miss. The authors suggest future extensions such as learnable attention weights for hyperedges, incorporation of macro‑economic indicators, and deployment in real‑time trading systems. Hermes thus represents a substantial step forward in leveraging higher‑order relational structures for financial time‑series forecasting.