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arxiv: 2509.23668 · v3 · submitted 2025-09-28 · 💻 cs.LG

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

Pith reviewed 2026-05-18 12:30 UTC · model grok-4.3

classification 💻 cs.LG
keywords stock time series forecastinghypergraph neural networkslead-lag interactionsmulti-scale modelingindustry correlationstemporal aggregation
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The pith

Hermes improves stock time series forecasts by capturing inter-industry lead-lag effects and multi-scale patterns through a hypergraph network.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Stock time series are shaped by correlations across industries, including cases where movements in one sector lead or lag others and where patterns appear at different time scales. Prior hypergraph methods capture these relationships only superficially and miss both the dynamic lead-lag structure and the multi-scale organization. Hermes introduces a hyperedge-based moving aggregation module that applies sliding windows and dynamic temporal aggregation to model flexible lead-lag dependencies among industries. It pairs this with cross-scale edge-to-edge message passing that fuses information across scales while keeping each scale internally consistent. Experiments on real stock datasets show the resulting model outperforms existing state-of-the-art forecasting methods.

Core claim

The Hermes framework improves exploitation of industry correlation in stock time series by integrating a hyperedge-based moving aggregation module, which uses a sliding window and dynamic temporal aggregation to capture inter-industry lead-lag interactions, together with cross-scale edge-to-edge message passing that integrates multi-scale information while preserving scale consistency.

What carries the argument

Hyperedge-based moving aggregation with sliding windows for lead-lag capture, combined with cross-scale edge-to-edge message passing for multi-scale fusion inside a spatial-temporal hypergraph network.

If this is right

  • More accurate modeling of dynamic temporal dependencies across industries in multivariate financial data.
  • Consistent integration of information at different temporal scales without loss of scale-specific structure.
  • Improved forecasting performance on real stock datasets compared with prior hypergraph and graph-based baselines.
  • Better support for decision-making by investors and analysts who rely on industry-level correlation signals.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same lead-lag and multi-scale mechanisms could be tested on other hierarchical time series such as supply-chain or commodity price data.
  • Combining the hypergraph structure with attention-based temporal encoders might further refine the capture of long-range dependencies.
  • Datasets that explicitly annotate industry hierarchies would allow direct measurement of how much the hypergraph representation contributes versus the aggregation rules.

Load-bearing premise

The accuracy gains come primarily from the two new modules rather than from other modeling choices or from particular properties of the stock datasets.

What would settle it

An ablation study that removes the moving aggregation module or the cross-scale message passing component and measures the resulting drop in forecasting accuracy on the same real-world stock datasets.

Figures

Figures reproduced from arXiv: 2509.23668 by Bin Yang, Chenjuan Guo, Christian S. Jensen, Ding Tu, Hanyin Cheng, Jilin Hu, Liu Yang, Rongjia Wu, Xiangfei Qiu, Xiangyu Xu, Xingjian Wu, Zhigang Zhang.

Figure 1
Figure 1. Figure 1: (a): Intra-industry correlation. Relations between stocks within an industry (hyperedge) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The architecture of Hermes. stock time series forecasting model that specifically takes into account the multi-scale nature of stock data, enabling it to capture the complexity of market dynamics more comprehensively. Furthermore, our approach places particular emphasis on the lead-lag relationships between financial industries, where the changes in one industry may precede or lag behind those in another. … view at source ↗
Figure 4
Figure 4. Figure 4: Three types of message passing: hy￾pernodes for stocks and hyperedges for indus￾tries. 8 16 32 64 Lookback window length 0.025 0.030 0.035 0.040 0.045 0.050 Information Coefficient (IC) NYSDAQ NYSE S&P500 (a) Lookback length 5 8 32 64 Latent space dimension 0.020 0.025 0.030 0.035 0.040 0.045 0.050 Information Coefficient (IC) NYSDAQ NYSE S&P500 (b) Latent space dimension [3, 3, 3] [9, 6, 3] [12, 4, 3] [12… view at source ↗
Figure 5
Figure 5. Figure 5: Parameter sensitivity studies of main hyper-parameters in Hermes. [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes Hermes, a multi-scale spatial-temporal hypergraph network for stock time series forecasting. It identifies limitations in prior hypergraph methods for capturing industry correlations—specifically, insufficient modeling of inter-industry lead-lag interactions and inadequate handling of multi-scale information within and across industries. The framework introduces a hyperedge-based moving aggregation module that uses a sliding window and dynamic temporal aggregation to address lead-lag dependencies, combined with cross-scale edge-to-edge message passing to integrate multi-scale information while preserving scale consistency. The central empirical claim is that these components enable Hermes to outperform existing state-of-the-art methods on multiple real-world stock datasets.

Significance. If the reported performance gains prove robust and are shown to arise specifically from the proposed modules rather than ancillary design choices, the work would advance hypergraph-based modeling for financial time series by providing a more flexible treatment of temporal lead-lag effects and hierarchical multi-scale structures. This could have practical value in a domain where even modest accuracy improvements carry economic significance.

major comments (2)
  1. [Experimental Results] Experimental section: The manuscript claims that Hermes outperforms SOTA methods on real-world stock datasets, yet no ablation results are presented that remove the hyperedge-based moving aggregation module (while holding hypergraph construction, loss, optimizer, and other components fixed) to isolate its contribution to any observed gains. Without such controls, attribution of improvements to the lead-lag modeling remains unverified and load-bearing for the central claim.
  2. [Methodology] Methodology section on multi-scale fusion: The cross-scale edge-to-edge message passing is presented as integrating information across scales while maintaining consistency, but the manuscript does not detail how the distinct scales are constructed or partitioned in the hypergraph (e.g., criteria for within-industry vs. among-industry scales or the number of scales). This definition is necessary to evaluate whether the module genuinely addresses the stated multi-scale limitation.
minor comments (2)
  1. [Abstract] The abstract summarizes the proposed modules and claims but omits any quantitative performance metrics or dataset names, which would aid immediate assessment even if full tables appear later.
  2. [Notation and Equations] Notation for hyperedges, sliding-window parameters, and scale indices should be introduced once and used consistently to prevent ambiguity in the equations describing aggregation and message passing.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback on our manuscript. We address each major comment below and outline the revisions we will make to strengthen the paper.

read point-by-point responses
  1. Referee: Experimental section: The manuscript claims that Hermes outperforms SOTA methods on real-world stock datasets, yet no ablation results are presented that remove the hyperedge-based moving aggregation module (while holding hypergraph construction, loss, optimizer, and other components fixed) to isolate its contribution to any observed gains. Without such controls, attribution of improvements to the lead-lag modeling remains unverified and load-bearing for the central claim.

    Authors: We agree that an ablation isolating the hyperedge-based moving aggregation module, with all other components held fixed, is necessary to rigorously attribute performance gains to the lead-lag modeling. We will add this controlled ablation experiment to the experimental section of the revised manuscript and report the corresponding results. revision: yes

  2. Referee: Methodology section on multi-scale fusion: The cross-scale edge-to-edge message passing is presented as integrating information across scales while maintaining consistency, but the manuscript does not detail how the distinct scales are constructed or partitioned in the hypergraph (e.g., criteria for within-industry vs. among-industry scales or the number of scales). This definition is necessary to evaluate whether the module genuinely addresses the stated multi-scale limitation.

    Authors: We acknowledge that explicit details on scale construction and partitioning are required for full reproducibility and evaluation. We will expand the methodology section to describe the criteria for defining within-industry versus among-industry scales, the number of scales used, and the partitioning approach in the hypergraph. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical architecture proposal with no derivational reduction

full rationale

The paper proposes the Hermes hypergraph framework with two new modules (hyperedge-based moving aggregation using sliding windows for lead-lag, and cross-scale edge-to-edge message passing) to better exploit industry correlations in stock time series. The central claim rests on experimental outperformance versus SOTA on real-world datasets. No equations, closed-form predictions, or first-principles derivations are presented that could reduce to fitted parameters or self-citations by construction. The work is self-contained as an empirical modeling contribution; any attribution of gains to the specific modules would require ablations (not a circularity concern). No load-bearing self-citation chains or ansatz smuggling appear in the provided text.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The paper introduces a new neural architecture whose performance claims rest on standard deep-learning assumptions plus two domain-specific modeling choices whose justification is not visible in the abstract.

free parameters (2)
  • hypergraph construction parameters
    Industry correlation thresholds or hyperedge definitions are not specified and must be chosen or learned.
  • sliding window size and aggregation weights
    These control the lead-lag modeling and are fitted or tuned on data.
axioms (1)
  • domain assumption Industry sectors form meaningful hyperedges that reflect lead-lag relationships in stock returns.
    Invoked when the authors state that exploiting industry correlation improves forecasting.

pith-pipeline@v0.9.0 · 5781 in / 1289 out tokens · 38098 ms · 2026-05-18T12:30:00.526645+00:00 · methodology

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    \@ifxundefined[1] #1\@undefined \@firstoftwo \@secondoftwo \@ifnum[1] #1 \@firstoftwo \@secondoftwo \@ifx[1] #1 \@firstoftwo \@secondoftwo [2] @ #1 \@temptokena #2 #1 @ \@temptokena \@ifclassloaded agu2001 natbib The agu2001 class already includes natbib coding, so you should not add it explicitly Type <Return> for now, but then later remove the command n...

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