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Topology data analysis of critical transitions in financial networks

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  • Marian Gidea

Abstract

We develop a topology data analysis-based method to detect early signs for critical transitions in financial data. From the time-series of multiple stock prices, we build time-dependent correlation networks, which exhibit topological structures. We compute the persistent homology associated to these structures in order to track the changes in topology when approaching a critical transition. As a case study, we investigate a portfolio of stocks during a period prior to the US financial crisis of 2007-2008, and show the presence of early signs of the critical transition.

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  • Marian Gidea, 2017. "Topology data analysis of critical transitions in financial networks," Papers 1701.06081, arXiv.org.
    • Handle: RePEc:arx:papers:1701.06081
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    1. Michael C. Munnix & Takashi Shimada & Rudi Schafer & Francois Leyvraz Thomas H. Seligman & Thomas Guhr & H. E. Stanley, 2012. "Identifying States of a Financial Market," Papers 1202.1623, arXiv.org.
    2. Ashadun Nobi & Sungmin Lee & Doo Hwan Kim & Jae Woo Lee, 2014. "Correlation and Network Topologies in Global and Local Stock Indices," Papers 1402.1552, arXiv.org.
    3. Matteo Smerlak & Brady Stoll & Agam Gupta & James S Magdanz, 2015. "Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-15, July.
    4. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
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    Cited by:

    1. Xiurong Chen & Aimin Hao & Yali Li, 2020. "The impact of financial contagion on real economy-An empirical research based on combination of complex network technology and spatial econometrics model," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-20, March.
    2. Krebs, Johannes, 2021. "On limit theorems for persistent Betti numbers from dependent data," Stochastic Processes and their Applications, Elsevier, vol. 139(C), pages 139-174.
    3. Buddha Nath Sharma & Anish Rai & SR Luwang & Md. Nurujjaman & Sushovan Majhi, 2025. "Causality Analysis of COVID-19 Induced Crashes in Stock and Commodity Markets: A Topological Perspective," Papers 2502.14431, arXiv.org.
    4. Luigi Caputi & Anna Pidnebesna & Jaroslav Hlinka, 2024. "Integral Betti signature confirms the hyperbolic geometry of brain, climate, and financial networks," Papers 2406.15505, arXiv.org.
    5. Guo, Hongfeng & Xia, Shengxiang & An, Qiguang & Zhang, Xin & Sun, Weihua & Zhao, Xinyao, 2020. "Empirical study of financial crises based on topological data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    6. Ismail, Mohd Sabri & Noorani, Mohd Salmi Md & Ismail, Munira & Razak, Fatimah Abdul & Alias, Mohd Almie, 2022. "Early warning signals of financial crises using persistent homology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    7. Gidea, Marian & Goldsmith, Daniel & Katz, Yuri & Roldan, Pablo & Shmalo, Yonah, 2020. "Topological recognition of critical transitions in time series of cryptocurrencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).
    8. Kulkarni, Saumitra & Pharasi, Hirdesh K. & Vijayaraghavan, Sudharsan & Kumar, Sunil & Chakraborti, Anirban & Samal, Areejit, 2024. "Investigation of Indian stock markets using topological data analysis and geometry-inspired network measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 643(C).
    9. Katz, Yuri A. & Biem, Alain, 2021. "Time-resolved topological data analysis of market instabilities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 571(C).
    10. Azamir, Bouchaib & Bennis, Driss & Michel, Bertrand, 2022. "A simplified algorithm for identifying abnormal changes in dynamic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    11. Guo, Hongfeng & Zhao, Xinyao & Yu, Hang & Zhang, Xin, 2021. "Analysis of global stock markets’ connections with emphasis on the impact of COVID-19," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    12. Anubha Goel & Damir Filipovi'c & Puneet Pasricha, 2024. "Sparse Portfolio Selection via Topological Data Analysis based Clustering," Papers 2401.16920, arXiv.org, revised Dec 2024.

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