Hierarchical Transformer Framework for Causal Discovery across Multi-Sector Financial Time Series

Authors

  • Lea Baumann
  • Martin Fischer
  • Nina Weber

DOI:

https://doi.org/10.54097/1v46hz47

Keywords:

Causal Discovery, Transformer Architecture, Hierarchical Attention, Financial Time Series, Multi-Sector Analysis, Temporal Causality

Abstract

Causal discovery in financial time series presents significant challenges due to the complex temporal dependencies and multi-sector interactions that characterize modern financial markets. Traditional statistical methods and conventional deep learning approaches often fail to capture the hierarchical nature of causal relationships across different market sectors and temporal scales. This paper proposes a novel Hierarchical Transformer Framework for Causal Discovery (HT-CD) that leverages multi-level attention mechanisms to identify causal relationships across multi-sector financial time series. Our framework introduces a sector-aware hierarchical encoder that processes financial data at multiple granularities, from individual asset-level patterns to sector-wide dynamics, while maintaining temporal consistency through specialized positional encoding schemes. The architecture incorporates a novel multi-head causal attention mechanism that explicitly models both contemporaneous and lagged causal effects across different sectors. Experimental evaluation on comprehensive financial datasets spanning multiple sectors demonstrates that HT-CD significantly outperforms existing causal discovery methods, achieving 23% improvement in causal structure accuracy while maintaining computational efficiency. The framework successfully identifies cross-sector causal relationships that align with established economic theories and provides interpretable insights into market contagion effects during financial stress periods.

References

[1] Esmalifalak, H., & Moradi‐Motlagh, A. (2025). Correlation networks in economics and finance: A review of methodologies and bibliometric analysis. Journal of Economic Surveys, 39(3), 1252-1286.

[2] Liu, X. (2025). Unraveling systemic risk transmission: An empirical exploration of network dynamics and market liquidity in the financial sector. Journal of the Knowledge Economy, 16(2), 6629-6664.

[3] Shojaie, A., & Fox, E. B. (2022). Granger causality: A review and recent advances. Annual Review of Statistics and Its Application, 9(1), 289-319.

[4] Kim, J., Kim, H., Kim, H., Lee, D., & Yoon, S. (2024). A Comprehensive Survey of Deep Learning for Time Series Forecasting: Architectural Diversity and Open Challenges. arXiv preprint arXiv:2411.05793.

[5] Mughal, M. F., Ansari, M., & Alam, M. (2025). Revolutionizing Financial Forecasting: The Rise of Transformer Models in Long-Term Time Series Analysis. AI-Driven Finance in the VUCA World, 142.

[6] Zheng, W., & Liu, W. (2025). Symmetry-Aware Transformers for Asymmetric Causal Discovery in Financial Time Series. Symmetry.

[7] Bi, Y., & Calhoun, V. D. (2025). The Financial Connectome: A Brain-Inspired Framework for Modeling Latent Market Dynamics. arXiv preprint arXiv:2508.02012.

[8] de Brito, M. M., Sodoge, J., Fekete, A., Hagenlocher, M., Koks, E., Kuhlicke, C., ... & Ward, P. J. (2024). Uncovering the dynamics of multi-sector impacts of hydrological extremes: A methods overview. Earth's Future, 12(1), e2023EF003906.

[9] Lommers, K., Harzli, O. E., & Kim, J. (2021). Confronting machine learning with financial research. arXiv preprint arXiv:2103.00366.

[10] Trabelsi, R. (2024). Sources of macroeconomic fluctuations in Tunisia: A structural VAR approach. SN Business & Economics, 4(10), 111.

[11] Das, J. D., Gedara, A. M., Bowala, S., Thulasiram, R. K., & Thavaneswaran, A. (2025, March). Non-Linear Data Representation with Machine Learning for Dynamic Covariance Based Financial Portfolio Optimization. In 2025 IEEE Symposium on Computational Intelligence for Financial Engineering and Economics (CiFer) (pp. 1-9). IEEE.

[12] Bystrova, D., Assaad, C. K., Arbel, J., Devijver, E., Gaussier, É., & Thuiller, W. (2023). Causal discovery from time series with hybrids of constraint-based and noise-based algorithms. arXiv preprint arXiv:2306.08765.

[13] Monti, R. P., Zhang, K., & Hyvärinen, A. (2020, August). Causal discovery with general non-linear relationships using non-linear ICA. In Uncertainty in artificial intelligence (pp. 186-195). PMLR.

[14] Ahmed, S., Nielsen, I. E., Tripathi, A., Siddiqui, S., Ramachandran, R. P., & Rasool, G. (2023). Transformers in time-series analysis: A tutorial. Circuits, Systems, and Signal Processing, 42(12), 7433-7466.

[15] Lezmi, E., & Xu, J. (2023). Time series forecasting with transformer models and application to asset management. Available at SSRN 4375798.

[16] Chen, S., Liu, Y., Zhang, Q., Shao, Z., & Wang, Z. (2025). Multi‐Distance Spatial-Temporal Graph Neural Network for Anomaly Detection in Blockchain Transactions. Advanced Intelligent Systems, 2400898.

[17] Zhang, X., Chen, S., Shao, Z., Niu, Y., & Fan, L. (2024). Enhanced Lithographic Hotspot Detection via Multi-Task Deep Learning with Synthetic Pattern Generation. IEEE Open Journal of the Computer Society.

[18] Zhang, Q., Chen, S., & Liu, W. (2025). Balanced Knowledge Transfer in MTTL-ClinicalBERT: A Symmetrical Multi-Task Learning Framework for Clinical Text Classification. Symmetry, 17(6), 823.

[19] Shao, Z., Wang, X., Ji, E., Chen, S., & Wang, J. (2025). GNN-EADD: Graph Neural Network-based E-commerce Anomaly Detection via Dual-stage Learning. IEEE Access.

[20] Li, P., Ren, S., Zhang, Q., Wang, X., & Liu, Y. (2024). Think4SCND: Reinforcement Learning with Thinking Model for Dynamic Supply Chain Network Design. IEEE Access.

[21] Liu, Y., Ren, S., Wang, X., & Zhou, M. (2024). Temporal logical attention network for log-based anomaly detection in distributed systems. Sensors, 24(24), 7949.

[22] Ren, S., Jin, J., Niu, G., & Liu, Y. (2025). ARCS: Adaptive Reinforcement Learning Framework for Automated Cybersecurity Incident Response Strategy Optimization. Applied Sciences, 15(2), 951.

[23] Cao, J., Zheng, W., Ge, Y., & Wang, J. (2025). DriftShield: Autonomous fraud detection via actor-critic reinforcement learning with dynamic feature reweighting. IEEE Open Journal of the Computer Society.

[24] Wang, J., Liu, J., Zheng, W., & Ge, Y. (2025). Temporal Heterogeneous Graph Contrastive Learning for Fraud Detection in Credit Card Transactions. IEEE Access.

[25] Mai, N. T., Cao, W., & Liu, W. (2025). Interpretable Knowledge Tracing via Transformer-Bayesian Hybrid Networks: Learning Temporal Dependencies and Causal Structures in Educational Data. Applied Sciences, 15(17), 9605.

[26] Cao, W., Mai, N. T., & Liu, W. (2025). Adaptive knowledge assessment via symmetric hierarchical Bayesian neural networks with graph symmetry-aware concept dependencies. Symmetry, 17(8), 1332.

[27] Mai, N. T., Cao, W., & Wang, Y. (2025). The global belonging support framework: Enhancing equity and access for international graduate students. Journal of International Students, 15(9), 141-160.

[28] Tan, Y., Wu, B., Cao, J., & Jiang, B. (2025). LLaMA-UTP: Knowledge-Guided Expert Mixture for Analyzing Uncertain Tax Positions. IEEE Access.

[29] Sun, T., Yang, J., Li, J., Chen, J., Liu, M., Fan, L., & Wang, X. (2024). Enhancing auto insurance risk evaluation with transformer and SHAP. IEEE Access.

[30] Ma, Z., Chen, X., Sun, T., Wang, X., Wu, Y. C., & Zhou, M. (2024). Blockchain-based zero-trust supply chain security integrated with deep reinforcement learning for inventory optimization. Future Internet, 16(5), 163.

[31] Zhang, H., Ge, Y., Zhao, X., & Wang, J. (2025). Hierarchical Deep Reinforcement Learning for Multi-Objective Integrated Circuit Physical Layout Optimization with Congestion-Aware Reward Shaping. IEEE Access.

[32] Ji, E., Wang, Y., Xing, S., & Jin, J. (2025). Hierarchical Reinforcement Learning for Energy-Efficient API Traffic Optimization in Large-Scale Advertising Systems. IEEE Access.

[33] Jin, J., Xing, S., Ji, E., & Liu, W. (2025). XGate: Explainable Reinforcement Learning for Transparent and Trustworthy API Traffic Management in IoT Sensor Networks. Sensors (Basel, Switzerland), 25(7), 2183.

Downloads

Published

30-09-2025

Issue

Section

Articles

How to Cite

Baumann, L., Fischer, M., & Weber, N. (2025). Hierarchical Transformer Framework for Causal Discovery across Multi-Sector Financial Time Series. Mathematical Modeling and Algorithm Application, 6(2), 8-14. https://doi.org/10.54097/1v46hz47