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Collective behavior of cryptocurrency price changes


  • Stosic, Darko
  • Stosic, Dusan
  • Ludermir, Teresa B.
  • Stosic, Tatijana


Digital assets termed cryptocurrencies are correlated. We analyze cross correlations between price changes of different cryptocurrencies using methods of random matrix theory and minimum spanning trees. We find that the cross correlation matrix exhibits non-trivial hierarchical structures and groupings of cryptocurrency pairs, which are not present in the partial cross correlations. In sharp contrast to the predictions for other financial markets, we discover that most of the eigenvalues in the spectrum of the cross correlation matrix do not agree with the universal predictions of random matrix theory, but the few of the largest eigenvalues deviate as expected. The minimum spanning tree of cryptocurrency cross correlations reveals distinct community structures that are surprisingly stable. Collective behaviors that are present in the cryptocurrency market can be useful for the construction of portfolio of cryptocurrencies as well as for future research on the subject.

Suggested Citation

  • Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Collective behavior of cryptocurrency price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 499-509.
  • Handle: RePEc:eee:phsmap:v:507:y:2018:i:c:p:499-509
    DOI: 10.1016/j.physa.2018.05.050

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    References listed on IDEAS

    1. repec:spr:jeicoo:v:12:y:2017:i:3:d:10.1007_s11403-016-0176-x is not listed on IDEAS
    2. 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.
    3. Plerou, V & Gopikrishnan, P & Rosenow, B & Amaral, L.A.N & Stanley, H.E, 2000. "A random matrix theory approach to financial cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 374-382.
    4. M. Potters & J. P. Bouchaud & L. Laloux, 2005. "Financial Applications of Random Matrix Theory: Old Laces and New Pieces," Papers physics/0507111,
    5. 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,
    6. 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.
    7. Wang, Gang-Jin & Xie, Chi & Chen, Shou & Yang, Jiao-Jiao & Yang, Ming-Yan, 2013. "Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3715-3730.
    8. Dong-Ming Song & Michele Tumminello & Wei-Xing Zhou & Rosario N. Mantegna, 2011. "Evolution of worldwide stock markets, correlation structure and correlation based graphs," Papers 1103.5555,
    9. Plerou, V. & Gopikrishnan, P. & Rosenow, B. & Amaral, L.A.N. & Stanley, H.E., 2001. "Collective behavior of stock price movements—a random matrix theory approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 175-180.
    10. J.-P. Bouchaud & L. Laloux & M. A. Miceli & M. Potters, 2007. "Large dimension forecasting models and random singular value spectra," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 201-207, January.
    11. Duan Wang & Boris Podobnik & Davor Horvati'c & H. Eugene Stanley, 2011. "Quantifying and Modeling Long-Range Cross-Correlations in Multiple Time Series with Applications to World Stock Indices," Papers 1102.2240,
    12. Nakamura, Tomomichi & Small, Michael, 2007. "Correlation structures in short-term variabilities of stock indices and exchange rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 96-101.
    13. S. Drozdz & A. Z. Gorski & J. Kwapien, 2007. "World currency exchange rate cross-correlations," Papers 0708.4347,
    14. repec:taf:quantf:v:17:y:2017:i:9:p:1417-1433 is not listed on IDEAS
    15. G. Oh & C. Eom & F. Wang & W.-S. Jung & H. E. Stanley & S. Kim, 2011. "Statistical properties of cross-correlation in the Korean stock market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 79(1), pages 55-60, January.
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    Cited by:

    1. Andr'es Garc'ia Medina & Graciela Gonz'alez-Far'ias, 2019. "Determining the number of factors in a forecast model by a random matrix test: cryptocurrencies," Papers 1905.00545,


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