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Rényi indices of financial minimum spanning trees

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  • Nie, Chun-Xiao
  • Song, Fu-Tie
  • Li, Sai-Ping

Abstract

The Rényi index is used here to describe topological structures of minimum spanning trees (MSTs) of financial markets. We categorize the topological structures of MSTs as dragon, star and super-star types. The MST based on Geometric Brownian motion is of dragon type, the MST constructed by One-Factor Model is super-star type, and most MSTs based on real market data belong to the star type. The Rényi index of the MST corresponding to S&P500 is evaluated, and the result shows that the Rényi index varies significantly in different time periods. In particular, it rose during crises and dropped when the S&P500 index rose significantly. A comparison study between the CSI300 index of the Chinese market and the S&P500 index shows that the MST structure of the CSI300 index varies more dramatically than the MST structure of the S&P500.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:883-889
    DOI: 10.1016/j.physa.2015.10.087
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    Cited by:

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    2. Nie, Chun-Xiao & Song, Fu-Tie, 2019. "Global Rényi index of the distance matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 902-915.
    3. Nie, Chun-Xiao & Song, Fu-Tie, 2018. "Analyzing the stock market based on the structure of kNN network," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 148-159.
    4. Chen, Jinyan & Nie, Chun-Xiao, 2024. "Impact of the collapse of silicon valley bank on the banking sector: An analysis based on nonlinear high-frequency networks," Finance Research Letters, Elsevier, vol. 62(PB).
    5. Nie, Chun-Xiao, 2022. "Generalized correlation dimension and heterogeneity of network spaces," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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