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Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks

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  • Heimo, Tapio
  • Kaski, Kimmo
  • Saramäki, Jari

Abstract

We study the time dependence of maximal spanning trees and asset graphs based on correlation matrices of stock returns. In these networks the nodes represent companies and links are related to the correlation coefficients between them. Special emphasis is given to the comparison between ordinary and denoised correlation matrices. The analysis of single- and multi-step survival ratios of the corresponding networks reveals that the ordinary correlation matrices are more stable in time than the denoised ones. Our study also shows that some information about the cluster structure of the companies is lost in the denoising procedure. Cluster structure that makes sense from an economic point of view exists, and can easily be observed in networks based on denoised correlation matrices. However, this structure is somewhat clearer in the networks based on ordinary correlation matrices. Some technical aspects, such as the random matrix denoising procedure, are also presented.

Suggested Citation

  • Heimo, Tapio & Kaski, Kimmo & Saramäki, Jari, 2009. "Maximal spanning trees, asset graphs and random matrix denoising in the analysis of dynamics of financial networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 145-156.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:2:p:145-156
    DOI: 10.1016/j.physa.2008.10.007
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906.
    2. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169, September.
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    Cited by:

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    2. 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.
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    4. Sindhuja Ranganathan & Mikko Kivelä & Juho Kanniainen, 2018. "Dynamics of investor spanning trees around dot-com bubble," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-14, June.
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    6. Yang, Chunxia & Zhu, Xueshuai & Li, Qian & Chen, Yanhua & Deng, Qiangqiang, 2014. "Research on the evolution of stock correlation based on maximal spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 1-18.
    7. Peng Yue & Qing Cai & Wanfeng Yan & Wei-Xing Zhou, 2020. "Information flow networks of Chinese stock market sectors," Papers 2004.08759, arXiv.org.
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    9. Raymond Ka-Kay Pang & Oscar Granados & Harsh Chhajer & Erika Fille Legara, 2020. "An analysis of network filtering methods to sovereign bond yields during COVID-19," Papers 2009.13390, arXiv.org, revised Feb 2021.
    10. Leonidas Sandoval Junior, 2012. "Survivability and centrality measures for networks of financial market indices," Papers 1201.4490, arXiv.org.
    11. Xingchen Wan & Jie Yang & Slavi Marinov & Jan-Peter Calliess & Stefan Zohren & Xiaowen Dong, 2020. "Sentiment Correlation in Financial News Networks and Associated Market Movements," Papers 2011.06430, arXiv.org, revised Feb 2021.
    12. Fatih Cavdur & Soundar Kumara, 2014. "Network mining: Applications to business data," Information Systems Frontiers, Springer, vol. 16(3), pages 473-490, July.
    13. Hu, Sen & Yang, Hualei & Cai, Boliang & Yang, Chunxia, 2013. "Research on spatial economic structure for different economic sectors from a perspective of a complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3682-3697.
    14. Zhang, Yiting & Lee, Gladys Hui Ting & Wong, Jian Cheng & Kok, Jun Liang & Prusty, Manamohan & Cheong, Siew Ann, 2011. "Will the US economy recover in 2010? A minimal spanning tree study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2020-2050.
    15. Leonidas Sandoval Junior, 2012. "To lag or not to lag? How to compare indices of stock markets that operate at different times," Papers 1201.4586, arXiv.org, revised Jul 2013.
    16. Stanislav S Borysov & Alexander V Balatsky, 2014. "Cross-Correlation Asymmetries and Causal Relationships between Stock and Market Risk," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-11, August.

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