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Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions

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  • Kullmann, L
  • Kertész, J
  • Mantegna, R.N

Abstract

The clustering of companies within a specific stock market index is studied by means of super-paramagnetic transitions of an appropriate q-state Potts model where the spins correspond to companies and the interactions are functions of the correlation coefficients determined from the time dependence of the companies’ individual stock prices. The method is a generalization of the clustering algorithm by Domany et al. to the case of anti-ferromagnetic interactions corresponding to anti-correlations. For the Dow Jones industrial average where no anti-correlations were observed in the investigated time period, the previous results obtained by different tools were well reproduced. For the Standard & Poor's 500, where anti-correlations occur, repulsion between stocks modify the cluster structure.

Suggested Citation

  • Kullmann, L & Kertész, J & Mantegna, R.N, 2000. "Identification of clusters of companies in stock indices via Potts super-paramagnetic transitions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 412-419.
    • Handle: RePEc:eee:phsmap:v:287:y:2000:i:3:p:412-419
    DOI: 10.1016/S0378-4371(00)00380-0
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    Cited by:

    1. khoojine, Arash Sioofy & Han, Dong, 2019. "Network analysis of the Chinese stock market during the turbulence of 2015–2016 using log-returns, volumes and mutual information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1091-1109.
    2. Challet, Damien & Bongiorno, Christian & Pelletier, Guillaume, 2021. "Financial factors selection with knockoffs: Fund replication, explanatory and prediction networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    3. Justo Puerto & Moises Rodr'iguez-Madrena & Andrea Scozzari, 2019. "Location and portfolio selection problems: A unified framework," Papers 1907.07101, arXiv.org.
    4. Yutong Lu & Gesine Reinert & Mihai Cucuringu, 2023. "Co-trading networks for modeling dynamic interdependency structures and estimating high-dimensional covariances in US equity markets," Papers 2302.09382, arXiv.org, revised May 2024.
    5. Yelibi, Lionel & Gebbie, Tim, 2020. "Fast Super-Paramagnetic Clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    6. Tanya Ara'ujo & Francisco Louc{c}~a, 2005. "The Geometry of Crashes - A Measure of the Dynamics of Stock Market Crises," Papers physics/0506137, arXiv.org, revised Jul 2005.
    7. Dieter Hendricks & Tim Gebbie & Diane Wilcox, 2015. "Detecting intraday financial market states using temporal clustering," Papers 1508.04900, arXiv.org, revised Feb 2017.
    8. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485, arXiv.org, revised Nov 2020.
    9. Musciotto, F. & Marotta, L. & Miccichè, S. & Mantegna, R.N., 2018. "Bootstrap validation of links of a minimum spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1032-1043.
    10. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    11. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    12. González-Solís, José Luis & Guizar-Ruiz, Juan Ignacio & Martínez-Espinosa, Juan Carlos & Martínez-Zerega, Brenda Esmeralda & Juárez-López, Héctor Alfonso & Vargas-Rodríguez, Héctor & Gallegos-Infante,, 2016. "Cancer detection based on Raman spectra super-paramagnetic clustering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 52-64.
    13. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    14. Siqueira, Erinaldo Leite & Stošić, Tatijana & Bejan, Lucian & Stošić, Borko, 2010. "Correlations and cross-correlations in the Brazilian agrarian commodities and stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2739-2743.
    15. Tanya Araujo & Francisco Louca, 2007. "The geometry of crashes. A measure of the dynamics of stock market crises," Quantitative Finance, Taylor & Francis Journals, vol. 7(1), pages 63-74.
    16. Yin, Yi & Shang, Pengjian, 2013. "Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6442-6457.

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