Complex Systems Theory and Crashes of Cryptocurrency Market

  • Vladimir N. Soloviev
  • Andriy BelinskiyEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1007)


This article demonstrates the possibility of constructing indicators of critical and crash phenomena in the volatile market of cryptocurrency. For this purpose, the methods of the theory of complex systems have been used. The possibility of constructing dynamic measures of complexity as recurrent, entropy, network, quantum behaving in a proper way during actual pre-crash periods has been shown. This fact is used to build predictors of crashes and critical events phenomena on the examples of all the patterns recorded in the time series of the key cryptocurrency Bitcoin, the effectiveness of the proposed indicators-precursors of these falls has been identified. From positions, attained by modern theoretical physics the concept of economic Planck’s constant has been proposed. The theory on the economic dynamic time series related to the cryptocurrencies market has been approved. Then, combining the empirical cross-correlation matrix with the random matrix theory, we mainly examine the statistical properties of cross-correlation coefficient, the evolution of the distribution of eigenvalues and corresponding eigenvectors of the global cryptocurrency market using the daily returns of 24 cryptocurrencies price time series all over the world from 2013 to 2018. The result has indicated that the largest eigenvalue reflects a collective effect of the whole market, and is very sensitive to the crash phenomena. It has been shown that both the introduced economic mass and the largest eigenvalue of the matrix of correlations can act like quantum indicator-predictors of falls in the market of cryptocurrencies.


Cryptocurrency Bitcoin Complex system Measures of complexity Crash Critical events Recurrence plot Recurrence quantification analysis Permutation entropy Complex networks Quantum econophysics Heisenberg uncertainty principle Random matrix theory Indicator-precursor 


  1. 1.
    Halvin, S., Cohen, R.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, New York (2010)Google Scholar
  2. 2.
    Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Newman, M., Watts, D., Barabási, A.-L.: The Structure and Dynamics of Networks. Princeton University Press, Princeton and Oxford (2006)zbMATHGoogle Scholar
  4. 4.
    Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Nikolis, G., Prigogine, I.: Exploring Complexity: An Introduction. W. H. Freeman and Company, New York (1989)Google Scholar
  6. 6.
    Andrews, B., Calder, M., Davis, R.: Maximumlikelihood estimation for α-stable autoregressive processes. Ann. Stat. 37, 1946–1982 (2009)CrossRefGoogle Scholar
  7. 7.
    Dassios, A., Li, L.: An economic bubble model and its first passage time. arXiv:1803.08160v1 [q-fin.MF]. Accessed 15 Sept 2018
  8. 8.
    Tarnopolski, M.: Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach. arXiv:1707.03746v3 [q-fin.CP]. Accessed 15 Sept 2018
  9. 9.
    Kodama, O., Pichl, L., Kaizoji, T.: Regime change and trend prediction for Bitcoin time series data. In: CBU International Conference on Innovations in Science and Education, Prague, pp. 384–388 (2017).,, Scholar
  10. 10.
    Shah, D., Zhang, K.: Bayesian: regression and Bitcoin. arXiv:1410.1231v1 [cs.AI]. Accessed 15 Oct 2018
  11. 11.
    Chen, T., Guestrin, C.: XGBoost: a scalable tree boosting system. In: Proceedings of the 22nd International Conference on Knowledge Discovery and Data Mining, pp. 785–794. ACM, San Francisco (2016)Google Scholar
  12. 12.
    Alessandretti, L., ElBahrawy, A., Aiello, L.M., Baronchelli, A.: Machine learning the cryptocurrency market. arXiv:1805.08550v1 [physics.soc-ph]. Accessed 15 Sept 2018
  13. 13.
    Guo, T., Antulov-Fantulin, N.: An experimental study of Bitcoin fluctuation using machine learning methods. arXiv:1802.04065v2 [stat.ML]. Accessed 15 Sept 2018
  14. 14.
    Albuquerque, P., de Sá, J., Padula, A., Montenegro, M.: The best of two worlds: forecasting high frequency volatility for cryptocurrencies and traditional currencies with support vector regression. Expert Syst. Appl. 97, 177–192 (2018). Scholar
  15. 15.
    Wang, M., et al.: A novel hybrid method of forecasting crude oil prices using complex network science and artificial intelligence algorithms. Appl. Energy 220, 480–495 (2018). Scholar
  16. 16.
    Kennis, M.: A Multi-channel online discourse as an indicator for Bitcoin price and volume. arXiv:1811.03146v1 [q-fin.ST]. Accessed 6 Nov 2018
  17. 17.
    Donier, J., Bouchaud, J.P.: Why do markets crash? Bitcoin data offers unprecedented insights. PLoS One 10(10), 1–11 (2015). Scholar
  18. 18.
    Bariviera, F.A., Zunino, L., Rosso, A.O.: An analysis of high-frequency cryptocurrencies price dynamics using permutation-information-theory quantifiers. Chaos 28(7), 07551 (2018). Scholar
  19. 19.
    Senroy, A.: The inefficiency of Bitcoin revisited: a high-frequency analysis with alternative currencies. Financ. Res. Lett. (2018).
  20. 20.
    Marwan, N., Schinkel, S., Kurths, J.: Recurrence plots 25 years later - gaining confidence in dynamical transitions. Europhys. Lett. 101(2), 20007 (2013). Scholar
  21. 21.
    Santos, T., Walk, S., Helic, D.: Nonlinear characterization of activity dynamics in online collaboration websites. In: Proceedings of the 26th International Conference on World Wide Web Companion, WWW 2017 Companion, Australia, pp. 1567–1572 (2017).
  22. 22.
    Di Francesco Maesa, D., Marino, A., Ricci, L.: Data-driven analysis of Bitcoin properties: exploiting the users graph. Int. J. Data Sci. Anal. 6(1), 63–80 (2018). Scholar
  23. 23.
    Bovet, A., Campajola, C., Lazo, J.F., et al.: Network-based indicators of Bitcoin bubbles. arXiv:1805.04460v1 [physics.soc-ph]. Accessed 11 Sept 2018
  24. 24.
    Kondor, D., Csabai, I., Szüle, J., Pόsfai, M., Vattay, G.: Infferring the interplay of network structure and market effects in Bitcoin. New J. Phys. 16, 125003 (2014). Scholar
  25. 25.
    Wheatley, S., Sornette, D., Huber, T., et al.: Are Bitcoin bubbles predictable? Combining a generalized Metcalfe’s law and the LPPLS model. arXiv:1803.05663v1 [econ.EM]. Accessed 15 Sept 2018
  26. 26.
    Gerlach, J-C., Demos, G., Sornette, D.: Dissection of Bitcoin’s multiscale bubble history from January 2012 to February 2018. arXiv:1804.06261v2 [econ.EM]. Accessed 15 Sept 2018
  27. 27.
    Soloviev, V., Belinskiy, A.: Methods of nonlinear dynamics and the construction of cryptocurrency crisis phenomena precursors. arXiv:1807.05837v1 [q-fin.ST]. Accessed 30 Sept 2018
  28. 28.
    Casey, M.B.: Speculative Bitcoin adoption/price theory. Accessed 25 Sept 2018
  29. 29.
    McComb, K.: Bitcoin crash: analysis of 8 historical crashes and what’s next. Accessed 25 Sept 2018
  30. 30.
    Amadeo, K.: Stock market corrections versus crashes and how to protect yourself: how you can tell if it’s a correction or a crash. Accessed 25 Sep 2018
  31. 31.
    Webber, C.L., Marwan, N. (eds.): Recurrence Plots and Their Quantifications: Expanding Horizons. Proceedings of the 6th International Symposium on Recurrence Plots, Grenoble, France, 17–19 June 2015, vol. 180, pp. 1–387. Springer, Heidelberg (2016). Scholar
  32. 32.
    Marwan, N., Wessel, N., Meyerfeldt, U., Schirdewan, A., Kurths, J.: Recurrence plot based measures of complexity and its application to heart rate variability data. Phys. Rev. E 66(2), 026702 (2002)CrossRefGoogle Scholar
  33. 33.
    Zbilut, J.P., Webber Jr., C.L.: Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A 171(3–4), 199–203 (1992)CrossRefGoogle Scholar
  34. 34.
    Webber Jr., C.L., Zbilut, J.P.: Dynamical assessment of physiological systems and states using recurrence plot strategies. J. Appl. Physiol. 76(2), 965–973 (1994)CrossRefGoogle Scholar
  35. 35.
    Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 2–4 (2002)CrossRefGoogle Scholar
  36. 36.
    Donner, R.V., Small, M., Donges, J.F., Marwan, N., et al.: Recurrence-based time series analysis by means of complex network methods. arXiv:1010.6032v1 [nlin.CD]. Accessed 25 Oct 2018
  37. 37.
    Lacasa, L., Luque, B., Ballesteros, F., et al.: From time series to complex networks: the visibility graph. PNAS 105(13), 4972–4975 (2008)MathSciNetCrossRefGoogle Scholar
  38. 38.
    Burnie, A.: Exploring the interconnectedness of cryptocurrencies using correlation networks. In: The Cryptocurrency Research Conference, pp. 1–29. Anglia Ruskin University, Cambridge (2018)Google Scholar
  39. 39.
    Mantegna, R.N., Stanley, H.E.: An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  40. 40.
    Maslov, V.P.: Econophysics and quantum statistics. Math. Notes 72, 811–818 (2002)MathSciNetCrossRefGoogle Scholar
  41. 41.
    Hidalgo, E.G.: Quantum Econophysics. arXiv:physics/0609245v1 [physics.soc-ph]. Accessed 15 Sept 2018
  42. 42.
    Saptsin, V., Soloviev, V.: Relativistic quantum econophysics - new paradigms in complex systems modelling. arXiv:0907.1142v1 [physics.soc-ph]. Accessed 25 Sept 2018
  43. 43.
    Colangelo, G., Clurana, F.M., Blanchet, L.C., Sewell, R.J., Mitchell, M.W.: Simultaneous tracking of spin angle and amplitude beyond classical limits. Nature 543, 525–528 (2017)CrossRefGoogle Scholar
  44. 44.
    Rodriguez, E.B., Aguilar, L.M.A.: Disturbance-disturbance uncertainty relation: the statistical distinguishability of quantum states determines disturbance. Sci. Rep. 8, 1–10 (2018)CrossRefGoogle Scholar
  45. 45.
    Rozema, L.A., Darabi, A., Mahler, D.H., Hayat, A., Soudagar, Y., Steinberg, A.M.: Violation of Heisenberg’s measurement-disturbance relationship by weak measurements. Phys. Rev. Lett. 109, 100404 (2012)CrossRefGoogle Scholar
  46. 46.
    Prevedel, R., Hamel, D.R., Colbeck, R., Fisher, K., Resch, K.J.: Experimental investigation of the uncertainty principle in the presence of quantum memory. Nat. Phys. 7(29), 757–761 (2011)CrossRefGoogle Scholar
  47. 47.
    Berta, M., Christandl, M., Colbeck, R., Renes, J., Renner, R.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6(9), 659–662 (2010)CrossRefGoogle Scholar
  48. 48.
    Landau, L.D., Lifshitis, E.M.: The Classical Theory of Fields. Course of Theoretical Physics. Butterworth-Heinemann, Oxford (1975)Google Scholar
  49. 49.
    Soloviev, V., Saptsin, V.: Heisenberg uncertainty principle and economic analogues of basic physical quantities. arXiv:1111.5289v1 [physics.gen-ph]. Accessed 15 Sept 2018
  50. 50.
    Soloviev, V.N., Romanenko, Y.V.: Economic analog of Heisenberg uncertainly principle and financial crisis. In: 20-th International Conference SAIT 2017, pp. 32–33. ESC “IASA” NTUU “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine (2017)Google Scholar
  51. 51.
    Soloviev, V.N., Romanenko, Y.V.: Economic analog of Heisenberg uncertainly principle and financial crisis. In: 20-th International Conference SAIT 2018, pp. 33–34. ESC “IASA” NTUU “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine (2018)Google Scholar
  52. 52.
    Wigner, E.P.: On a class of analytic functions from the quantum theory of collisions. Ann. Math. 53, 36–47 (1951)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Dyson, F.J.: Statistical theory of the energy levels of complex systems. J. Math. Phys. 3, 140–156 (1962)MathSciNetCrossRefGoogle Scholar
  54. 54.
    Mehta, L.M.: Random Matrices. Academic Press, San Diego (1991)zbMATHGoogle Scholar
  55. 55.
    Laloux, L., Cizeau, P., Bouchaud, J.-P., Potters, M.: Noise dressing of financial correlation matrices. Phys. Rev. Lett. 83, 1467–1470 (1999)CrossRefGoogle Scholar
  56. 56.
    Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Guhr, T., Stanley, H.E.: Random matrix approach to cross correlations in financial data. Phys. Rev. E 65, 066126 (2002)CrossRefGoogle Scholar
  57. 57.
    Shen, J., Zheng, B.: Cross-correlation in financial dynamics. EPL (Europhys. Lett.) 86, 48005 (2009)CrossRefGoogle Scholar
  58. 58.
    Jiang, S., Guo, J., Yang, C., Tian, L.: Random matrix analysis of cross-correlation in energy market of Shanxi, random matrix analysis of cross-correlation in energy market of Shanxi, China. Int. J. Nonlinear Sci. 23(2), 96–101 (2017)MathSciNetGoogle Scholar
  59. 59.
    Urama, T.C., Ezepue, P.O., Nnanwa, C.P.: Analysis of cross-correlations in emerging markets using random matrix theory. J. Math. Financ. 7, 291–307 (2017)CrossRefGoogle Scholar
  60. 60.
    Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Kryvyi Rih State Pedagogical UniversityKryvyi RihUkraine

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