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Fractal structure in the S&P500: A correlation-based threshold network approach

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  • Ku, Seungmo
  • Lee, Changju
  • Chang, Woojin
  • Wook Song, Jae

Abstract

This research aims to analyze the S&P500 network, one of the representatives of the global financial market, based on its network fractality. The research is conducted in the following steps. At first, we propose the concept of a correlation-based threshold network based on minimum spanning tree. Secondly, we investigate the fractal dimension of threshold networks and propose suitable fractal dimension measures. Lastly, we analyze the S&P500 network based on the proposed measures and utilize them in the market prediction. Based on the results, we discover the self-similarity characteristic of the S&P500 network, where a strong effective repulsion phenomenon is detected. Furthermore, we observe the different growth patterns of S&P500 network for different combinations of fractal conditions defined by the proposed measures. Then, we utilize the measures in the prediction of the cumulative log-return of S&P500 index via a simple artificial neural network and detect the improvement of prediction performance in the long-term development of the market.

Suggested Citation

  • Ku, Seungmo & Lee, Changju & Chang, Woojin & Wook Song, Jae, 2020. "Fractal structure in the S&P500: A correlation-based threshold network approach," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
  • Handle: RePEc:eee:chsofr:v:137:y:2020:i:c:s0960077920302484
    DOI: 10.1016/j.chaos.2020.109848
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    as
    1. Maasoumi, Esfandiar & Racine, Jeff, 2002. "Entropy and predictability of stock market returns," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 291-312, March.
    2. Gang-Jin Wang & Chi Xie & Shou Chen, 2017. "Multiscale correlation networks analysis of the US stock market: a wavelet analysis," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(3), pages 561-594, October.
    3. 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.
    4. 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.
    5. 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.
    6. Longin, Francois & Solnik, Bruno, 1995. "Is the correlation in international equity returns constant: 1960-1990?," Journal of International Money and Finance, Elsevier, vol. 14(1), pages 3-26, February.
    7. Guida, Michele & Maria, Funaro, 2007. "Topology of the Italian airport network: A scale-free small-world network with a fractal structure?," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 527-536.
    8. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    9. Boginski, Vladimir & Butenko, Sergiy & Pardalos, Panos M., 2005. "Statistical analysis of financial networks," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 431-443, February.
    10. Santos, N.M. & Santos, D.M.F., 2018. "A fractal dimension minimum in electrodeposited copper dendritic patterns," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 381-385.
    11. Darbellay, Georges A & Wuertz, Diethelm, 2000. "The entropy as a tool for analysing statistical dependences in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 429-439.
    12. Lahmiri, Salim & Bekiros, Stelios, 2019. "Cryptocurrency forecasting with deep learning chaotic neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 35-40.
    13. Song, Yu & Akagi, Fumio, 2016. "Application of artificial neural network for the prediction of stock market returns: The case of the Japanese stock marketAuthor-Name: Qiu, Mingyue," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 1-7.
    14. 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.
    15. Gang-Jin Wang & Chi Xie & Kaijian He & H. Eugene Stanley, 2017. "Extreme risk spillover network: application to financial institutions," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1417-1433, September.
    16. Dror Y Kenett & Michele Tumminello & Asaf Madi & Gitit Gur-Gershgoren & Rosario N Mantegna & Eshel Ben-Jacob, 2010. "Dominating Clasp of the Financial Sector Revealed by Partial Correlation Analysis of the Stock Market," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-14, December.
    17. Nie, Chun-Xiao, 2019. "Applying correlation dimension to the analysis of the evolution of network structure," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 294-303.
    18. Chai, Soo H. & Lim, Joon S., 2016. "Forecasting business cycle with chaotic time series based on neural network with weighted fuzzy membership functions," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 118-126.
    19. Caraiani, Petre, 2014. "The predictive power of singular value decomposition entropy for stock market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 571-578.
    20. Patro, Dilip K. & Qi, Min & Sun, Xian, 2013. "A simple indicator of systemic risk," Journal of Financial Stability, Elsevier, vol. 9(1), pages 105-116.
    21. Li, Dongyan & Wang, Xingyuan & Huang, Penghe, 2017. "A fractal growth model: Exploring the connection pattern of hubs in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 200-211.
    22. Xin-Jian Xu & Kuo Wang & Liucun Zhu & Li-Jie Zhang, 2018. "Efficient construction of threshold networks of stock markets," Papers 1803.06223, arXiv.org, revised Aug 2018.
    23. Xu, Xin-Jian & Wang, Kuo & Zhu, Liucun & Zhang, Li-Jie, 2018. "Efficient construction of threshold networks of stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1080-1086.
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    1. Cho, Younghwan & Song, Jae Wook, 2023. "Hierarchical risk parity using security selection based on peripheral assets of correlation-based minimum spanning trees," Finance Research Letters, Elsevier, vol. 53(C).

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