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Studying the correlation structure based on market geometry

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  • Chun-Xiao Nie

    (Zhejiang Gongshang University)

Abstract

Network methods can extract the structure of financial correlation matrices, and market geometry reconstructs the correlation relationship by constructing a vector set in the Euclidean space. This study uses a geometric perspective to analyse financial networks and examine the relationship between correlation structures and geometric conditions. Based on the concept of Euclidean space, we can naturally define geometric concepts such as stock vector and inner product between stocks. The analysis reveals that the structure of the financial correlation network is significantly affected by geometric conditions. We use stock market data to construct networks with different structures, such as a network with a hub node. We find that some stocks with small vector norms have an important effect on changes in network structure. In addition, we define a dimension to describe the correlation information included in the subspace of the market space and find that the dynamics of the dimension are related to the market state. This paper establishes a way to study network structure through market geometry, thereby providing a new method of correlation analysis.

Suggested Citation

  • Chun-Xiao Nie, 2021. "Studying the correlation structure based on market geometry," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 16(2), pages 411-441, April.
    • Handle: RePEc:spr:jeicoo:v:16:y:2021:i:2:d:10.1007_s11403-020-00305-2
    DOI: 10.1007/s11403-020-00305-2
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    1. M. Wili'nski & A. Sienkiewicz & T. Gubiec & R. Kutner & Z. R. Struzik, 2013. "Structural and topological phase transitions on the German Stock Exchange," Papers 1301.2530, arXiv.org, revised Jul 2013.
    2. Sunil Kumar & Nivedita Deo, 2012. "Correlation, Network and Multifractal Analysis of Global Financial Indices," Papers 1202.0409, arXiv.org.
    3. Wiliński, M. & Sienkiewicz, A. & Gubiec, T. & Kutner, R. & Struzik, Z.R., 2013. "Structural and topological phase transitions on the German Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5963-5973.
    4. Wang, Gang-Jin & Xie, Chi, 2015. "Correlation structure and dynamics of international real estate securities markets: A network perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 176-193.
    5. Nie, Chun-Xiao & Song, Fu-Tie & Li, Sai-Ping, 2016. "Rényi indices of financial minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 883-889.
    6. Nie, Chun-Xiao & Song, Fu-Tie, 2018. "Constructing financial network based on PMFG and threshold method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 104-113.
    7. Vasiliki Plerou & Parameswaran Gopikrishnan & Bernd Rosenow & Luis A. Nunes Amaral & H. Eugene Stanley, 1999. "Universal and non-universal properties of cross-correlations in financial time series," Papers cond-mat/9902283, arXiv.org.
    8. Gema Fernández-Avilés & José-María Montero & Lidia Sanchis-Marco, 2020. "Extreme downside risk co-movement in commodity markets during distress periods: a multidimensional scaling approach," The European Journal of Finance, Taylor & Francis Journals, vol. 26(12), pages 1207-1237, August.
    9. M. Tumminello & T. Di Matteo & T. Aste & R. N. Mantegna, 2007. "Correlation based networks of equity returns sampled at different time horizons," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 209-217, January.
    10. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    11. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
    12. Yang, Yue & Yang, Huijie, 2008. "Complex network-based time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1381-1386.
    13. David Matesanz & Guillermo Ortega, 2014. "Network analysis of exchange data: interdependence drives crisis contagion," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(4), pages 1835-1851, July.
    14. Jung, Woo-Sung & Chae, Seungbyung & Yang, Jae-Suk & Moon, Hie-Tae, 2006. "Characteristics of the Korean stock market correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 263-271.
    15. Garas, Antonios & Argyrakis, Panos, 2007. "Correlation study of the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 399-410.
    16. Sensoy, A. & Yuksel, S. & Erturk, M., 2013. "Analysis of cross-correlations between financial markets after the 2008 crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 5027-5045.
    17. Conlon, T. & Ruskin, H.J. & Crane, M., 2009. "Cross-correlation dynamics in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 705-714.
    18. Harnchai Eng-Uthaiwat, 2018. "Stock market return predictability: Does network topology matter?," Review of Quantitative Finance and Accounting, Springer, vol. 51(2), pages 433-460, August.
    19. Groenen, Patrick J. F. & Franses, Philip Hans, 2000. "Visualizing time-varying correlations across stock markets," Journal of Empirical Finance, Elsevier, vol. 7(2), pages 155-172, August.
    20. Gang-Jin Wang & Chi Xie & H. Eugene Stanley, 2018. "Correlation Structure and Evolution of World Stock Markets: Evidence from Pearson and Partial Correlation-Based Networks," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 607-635, March.
    21. Araújo, Tanya & Dias, João & Eleutério, Samuel & Louçã, Francisco, 2013. "A measure of multivariate kurtosis for the identification of the dynamics of a N-dimensional market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3708-3714.
    22. Joël Bun & Jean-Philippe Bouchaud & Marc Potters, 2017. "Cleaning large correlation matrices: tools from random matrix theory," Post-Print hal-01491304, HAL.
    23. 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.
    24. Giuseppe Buccheri & Stefano Marmi & Rosario N. Mantegna, 2013. "Evolution of correlation structure of industrial indices of US equity markets," Papers 1306.4769, arXiv.org.
    25. Eliazar, Iddo, 2011. "Randomness, evenness, and Rényi’s index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 1982-1990.
    26. Vilela Mendes, R. & Araújo, Tanya & Louçã, Francisco, 2003. "Reconstructing an economic space from a market metric," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 635-650.
    27. Irena Vodenska & Alexander P. Becker & Di Zhou & Dror Y. Kenett & H. Eugene Stanley & Shlomo Havlin, 2016. "Community Analysis of Global Financial Markets," Risks, MDPI, vol. 4(2), pages 1-15, May.
    28. Peralta, Gustavo & Zareei, Abalfazl, 2016. "A network approach to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 38(PA), pages 157-180.
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    1. Nie, Chun-Xiao & Song, Fu-Tie, 2023. "Stable versus fragile community structures in the correlation dynamics of Chinese industry indices," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).

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