Abstract
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.
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References
Halvin, S., Cohen, R.: Complex Networks: Structure, Robustness and Function. Cambridge University Press, New York (2010)
Albert, R., Barabási, A.-L.: Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)
Newman, M., Watts, D., Barabási, A.-L.: The Structure and Dynamics of Networks. Princeton University Press, Princeton and Oxford (2006)
Newman, M.E.J.: The structure and function of complex networks. SIAM Rev. 45(2), 167–256 (2003)
Nikolis, G., Prigogine, I.: Exploring Complexity: An Introduction. W. H. Freeman and Company, New York (1989)
Andrews, B., Calder, M., Davis, R.: Maximumlikelihood estimation for α-stable autoregressive processes. Ann. Stat. 37, 1946–1982 (2009)
Dassios, A., Li, L.: An economic bubble model and its first passage time. arXiv:1803.08160v1 [q-fin.MF]. Accessed 15 Sept 2018
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
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). www.cbuni.cz, www.journals.cz, https://doi.org/10.12955/cbup.v5.954
Shah, D., Zhang, K.: Bayesian: regression and Bitcoin. arXiv:1410.1231v1 [cs.AI]. Accessed 15 Oct 2018
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)
Alessandretti, L., ElBahrawy, A., Aiello, L.M., Baronchelli, A.: Machine learning the cryptocurrency market. arXiv:1805.08550v1 [physics.soc-ph]. Accessed 15 Sept 2018
Guo, T., Antulov-Fantulin, N.: An experimental study of Bitcoin fluctuation using machine learning methods. arXiv:1802.04065v2 [stat.ML]. Accessed 15 Sept 2018
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). https://doi.org/10.1016/j.eswa.2017.12.004
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). https://doi.org/10.1016/j.apenergy.2018.03.148
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
Donier, J., Bouchaud, J.P.: Why do markets crash? Bitcoin data offers unprecedented insights. PLoS One 10(10), 1–11 (2015). https://doi.org/10.1371/journal.pone.0139356
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). https://doi.org/10.1063/1.5027153
Senroy, A.: The inefficiency of Bitcoin revisited: a high-frequency analysis with alternative currencies. Financ. Res. Lett. (2018). https://doi.org/10.1016/j.frl.2018.04.002
Marwan, N., Schinkel, S., Kurths, J.: Recurrence plots 25 years later - gaining confidence in dynamical transitions. Europhys. Lett. 101(2), 20007 (2013). https://doi.org/10.1209/0295-5075/101/20007
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). https://doi.org/10.1145/3041021.3051117
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). https://doi.org/10.1007/s41060-017-0074-x
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
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). https://doi.org/10.1088/1367-2630/16/12/125003
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
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
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
Casey, M.B.: Speculative Bitcoin adoption/price theory. https://medium.com/@mcasey0827/speculative-bitcoin-adoption-price-theory-2eed48ecf7da. Accessed 25 Sept 2018
McComb, K.: Bitcoin crash: analysis of 8 historical crashes and what’s next. https://blog.purse.io/bitcoin-crash-e112ee42c0b5. Accessed 25 Sept 2018
Amadeo, K.: Stock market corrections versus crashes and how to protect yourself: how you can tell if it’s a correction or a crash. https://www.thebalance.com/stock-market-correction-3305863. Accessed 25 Sep 2018
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). https://doi.org/10.1007/978-3-319-29922-8
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)
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)
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)
Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88(17), 2–4 (2002)
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
Lacasa, L., Luque, B., Ballesteros, F., et al.: From time series to complex networks: the visibility graph. PNAS 105(13), 4972–4975 (2008)
Burnie, A.: Exploring the interconnectedness of cryptocurrencies using correlation networks. In: The Cryptocurrency Research Conference, pp. 1–29. Anglia Ruskin University, Cambridge (2018)
Mantegna, R.N., Stanley, H.E.: An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (2000)
Maslov, V.P.: Econophysics and quantum statistics. Math. Notes 72, 811–818 (2002)
Hidalgo, E.G.: Quantum Econophysics. arXiv:physics/0609245v1 [physics.soc-ph]. Accessed 15 Sept 2018
Saptsin, V., Soloviev, V.: Relativistic quantum econophysics - new paradigms in complex systems modelling. arXiv:0907.1142v1 [physics.soc-ph]. Accessed 25 Sept 2018
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)
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)
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)
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)
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)
Landau, L.D., Lifshitis, E.M.: The Classical Theory of Fields. Course of Theoretical Physics. Butterworth-Heinemann, Oxford (1975)
Soloviev, V., Saptsin, V.: Heisenberg uncertainty principle and economic analogues of basic physical quantities. arXiv:1111.5289v1 [physics.gen-ph]. Accessed 15 Sept 2018
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)
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)
Wigner, E.P.: On a class of analytic functions from the quantum theory of collisions. Ann. Math. 53, 36–47 (1951)
Dyson, F.J.: Statistical theory of the energy levels of complex systems. J. Math. Phys. 3, 140–156 (1962)
Mehta, L.M.: Random Matrices. Academic Press, San Diego (1991)
Laloux, L., Cizeau, P., Bouchaud, J.-P., Potters, M.: Noise dressing of financial correlation matrices. Phys. Rev. Lett. 83, 1467–1470 (1999)
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)
Shen, J., Zheng, B.: Cross-correlation in financial dynamics. EPL (Europhys. Lett.) 86, 48005 (2009)
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)
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)
Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492 (1958)
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Soloviev, V.N., Belinskiy, A. (2019). Complex Systems Theory and Crashes of Cryptocurrency Market. In: Ermolayev, V., Suárez-Figueroa, M., Yakovyna, V., Mayr, H., Nikitchenko, M., Spivakovsky, A. (eds) Information and Communication Technologies in Education, Research, and Industrial Applications. ICTERI 2018. Communications in Computer and Information Science, vol 1007. Springer, Cham. https://doi.org/10.1007/978-3-030-13929-2_14
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