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Spectral and network methods in the analysis of correlation matrices of stock returns

Author

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  • Heimo, Tapio
  • Saramäki, Jari
  • Onnela, Jukka-Pekka
  • Kaski, Kimmo

Abstract

Correlation matrices inferred from stock return time series contain information on the behaviour of the market, especially on clusters of highly correlating stocks. Here we study a subset of New York Stock Exchange (NYSE) traded stocks and compare three different methods of analysis: (i) spectral analysis, i.e. investigation of the eigenvalue–eigenvector pairs of the correlation matrix, (ii) asset trees, obtained by constructing the maximal spanning tree of the correlation matrix, and (iii) asset graphs, which are networks in which the strongest correlations are depicted as edges. We illustrate and discuss the localisation of the most significant modes of fluctuation, i.e. eigenvectors corresponding to the largest eigenvalues, on the asset trees and graphs.

Suggested Citation

  • Heimo, Tapio & Saramäki, Jari & Onnela, Jukka-Pekka & Kaski, Kimmo, 2007. "Spectral and network methods in the analysis of correlation matrices of stock returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 147-151.
    • Handle: RePEc:eee:phsmap:v:383:y:2007:i:1:p:147-151
    DOI: 10.1016/j.physa.2007.04.124
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    Citations

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    Cited by:

    1. Coletti, Paolo, 2016. "Comparing minimum spanning trees of the Italian stock market using returns and volumes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 246-261.
    2. Bommarito, Michael J. & Duran, Ahmet, 2018. "Spectral analysis of time-dependent market-adjusted return correlation matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 273-282.
    3. Li, Yan & Jiang, Xiong-Fei & Tian, Yue & Li, Sai-Ping & Zheng, Bo, 2019. "Portfolio optimization based on network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 671-681.
    4. Peng Yue & Qing Cai & Wanfeng Yan & Wei-Xing Zhou, 2020. "Information flow networks of Chinese stock market sectors," Papers 2004.08759, arXiv.org.
    5. 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.
    6. Yusuf Yargı BAYDİLLİ & Şafak BAYIR & İlker TÜRKER, 2017. "A Hierarchical View of a National Stock Market as a Complex Network," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(1), pages 205-222.
    7. Lee, Junghoon & Youn, Janghyuk & Chang, Woojin, 2012. "Intraday volatility and network topological properties in the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1354-1360.
    8. Akgüller, Ömer & Balcı, Mehmet Ali, 2018. "Geodetic convex boundary curvatures of the communities in stock market networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 569-581.
    9. 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.
    10. Chakrabarti, Arnab & Chakrabarti, Anindya S., 2020. "Fractional Differencing: (In)stability of Spectral Structure and Risk Measures of Financial Networks," IIMA Working Papers WP 2020-07-01, Indian Institute of Management Ahmedabad, Research and Publication Department.

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