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Clustering and information in correlation based financial networks

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  • J.-P. Onnela
  • K. Kaski
  • J. Kertész

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    Abstract

    Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to select the relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graph with no edges where the vertices correspond to stocks. Then, one by one, we insert edges between the vertices according to the rank of their correlation strength, resulting in a network called asset graph. We study its properties, such as topologically different growth types, number and size of clusters and clustering coefficient. These properties, calculated from empirical data, are compared against those of a random graph. The growth of the graph can be classified according to the topological role of the newly inserted edge. We find that the type of growth which is responsible for creating cycles in the graph sets in much earlier for the empirical asset graph than for the random graph, and thus reflects the high degree of networking present in the market. We also find the number of clusters in the random graph to be one order of magnitude higher than for the asset graph. At a critical threshold, the random graph undergoes a radical change in topology related to percolation transition and forms a single giant cluster, a phenomenon which is not observed for the asset graph. Differences in mean clustering coefficient lead us to conclude that most information is contained roughly within 10% of the edges. Copyright Springer-Verlag Berlin/Heidelberg 2004

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    File URL: http://hdl.handle.net/10.1140/epjb/e2004-00128-7
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    Bibliographic Info

    Article provided by Springer in its journal The European Physical Journal B - Condensed Matter and Complex Systems.

    Volume (Year): 38 (2004)
    Issue (Month): 2 (03)
    Pages: 353-362

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    Handle: RePEc:spr:eurphb:v:38:y:2004:i:2:p:353-362

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    Web page: http://www.springer.com/economics/journal/10051

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    References

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    1. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
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    Cited by:
    1. Sandoval, Leonidas, 2014. "To lag or not to lag? How to compare indices of stock markets that operate on different times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 227-243.
    2. Gorban, Alexander N. & Smirnova, Elena V. & Tyukina, Tatiana A., 2010. "Correlations, risk and crisis: From physiology to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3193-3217.
    3. Bolgorian, Meysam & Raei, Reza, 2010. "Convergence of fundamentalists and chartists’ expectations: An alarm for stock market crash," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3822-3827.
    4. Tse, Chi K. & Liu, Jing & Lau, Francis C.M., 2010. "A network perspective of the stock market," Journal of Empirical Finance, Elsevier, vol. 17(4), pages 659-667, September.
    5. Lyócsa, Štefan & Výrost, Tomáš & Baumöhl, Eduard, 2012. "Stock market networks: The dynamic conditional correlation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4147-4158.
    6. Wang, Junjie & Zhou, Shuigeng & Guan, Jihong, 2011. "Characteristics of real futures trading networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 398-409.
    7. Vizgunov, A. & Goldengorin, B. & Zamaraev, V. & Kalyagin, V. & Koldanov, A. & Koldanov, P. & Pardalos, P., 2012. "Applying Market Graphs for Russian Stock Market Analysis," Journal of the New Economic Association, New Economic Association, vol. 15(3), pages 66-81.
    8. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2011. "The Japanese economy in crises: A time series segmentation study," Economics Discussion Papers 2011-24, Kiel Institute for the World Economy.
    9. Tu, Chengyi, 2014. "Cointegration-based financial networks study in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 245-254.
    10. Shu-Heng Chen & Sai-Ping Li, 2011. "Econophysics: Bridges over a Turbulent Current," Papers 1107.5373, arXiv.org.
    11. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    12. Yang, Chunxia & Chen, Yanhua & Niu, Lei & Li, Qian, 2014. "Cointegration analysis and influence rank—A network approach to global stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 168-185.
    13. Sandoval, Leonidas, 2012. "Pruning a minimum spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2678-2711.
    14. Jarosław Kwapień & Sylwia Gworek & Stanisław Drożdż & Andrzej Górski, 2009. "Analysis of a network structure of the foreign currency exchange market," Journal of Economic Interaction and Coordination, Springer, vol. 4(1), pages 55-72, June.
    15. Leonidas Sandoval Junior, 2011. "A Map of the Brazilian Stock Market," Papers 1107.4146, arXiv.org, revised Mar 2013.
    16. Grigory Bautin & Valery Kalyagin & Alexander Koldanov & Petr Koldanov & Panos Pardalos, 2013. "Simple measure of similarity for the market graph construction," Computational Management Science, Springer, vol. 10(2), pages 105-124, June.
    17. Výrost, Tomáš, 2012. "Country effects in CEE3 stock market networks: a preliminary study," MPRA Paper 43481, University Library of Munich, Germany.

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