Будь ласка, використовуйте цей ідентифікатор, щоб цитувати або посилатися на цей матеріал: http://elibrary.kdpu.edu.ua/xmlui/handle/123456789/6974
Назва: Econophysics of cryptocurrency crashes: a systematic review
Автори: Bielinskyi, Andrii O.
Serdyuk, Oleksandr A.
Семеріков, Сергій Олексійович
Соловйов, Володимир Миколайович
Білінський, Андрій Іванович
Сердюк, О. А.
Ключові слова: blockchain
cryptocurrency market
indicators-precursors of crisis phenomena
econophysics
Дата публікації: 18-гру-2021
Бібліографічний опис: Bielinskyi A. O. Econophysics of cryptocurrency crashes: a systematic review [Electronic resource] / Andrii O. Bielinskyi, Oleksandr A. Serdyuk, Serhiy O. Semerikov, Vladimir N. Soloviev // Proceedings of the Selected and Revised Papers of 9th International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2-MLPEED 2021). Odessa, Ukraine, May 26-28, 2021 / Edited by : Arnold E. Kiv, Vladimir N. Soloviev, Serhiy O. Semerikov // CEUR Workshop Proceedings. – 2021. – Vol. 3048. – P. 31-133. – Access mode : http://ceur-ws.org/Vol-3048/paper03.pdf
Короткий огляд (реферат): Cryptocurrencies refer to a type of digital asset that uses distributed ledger, or blockchain technology to enable a secure transaction. Like other financial assets, they show signs of complex systems built from a large number of nonlinearly interacting constituents, which exhibits collective behavior and, due to an exchange of energy or information with the environment, can easily modify its internal structure and patterns of activity. We review the econophysics analysis methods and models adopted in or invented for financial time series and their subtle properties, which are applicable to time series in other disciplines. Quantitative measures of complexity have been proposed, classified, and adapted to the cryptocurrency market. Their behavior in the face of critical events and known cryptocurrency market crashes has been analyzed. It has been shown that most of these measures behave characteristically in the periods preceding the critical event. Therefore, it is possible to build indicators-precursors of crisis phenomena in the cryptocurrency market.
Опис: [1] R. Albert, A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74 (2002) 47–97. doi: 10.1103/RevModPhys.74.47 . [2] C. Reuven, H. Shlomo, Complex Networks: Structure, Robustness and Function, Cambridge University Press, 2010. [3] M. E. J. Newman, The structure and function of complex networks, SIAM Review 45 (2003) 167–256. doi: 10.1137/s003614450342480 . [4] M. Newman, A.-L. Barabasi, D. J. Watts (Eds.), The Structure and Dynamics of Networks, Princeton University Press, Princeton, NJ, USA, 2006. [5] G. Nicolis, I. Prigogine, Exploring complexity: an introduction, W.H. Freeman, 1989. [6] A. Rai, A. Mahata, M. Nurujjaman, O. Prakash, Statistical properties of the aftershocks of stock market crashes: evidence based on the 1987 crash, 2008 financial crisis and COVID-19 pandemic, 2020. arXiv:2012.03012 . [7] E. Mnif, A. Jarboui, K. Mouakhar, How the cryptocurrency market has performed during COVID 19? A multifractal analysis, Finance Research Letters 36 (2020) 101647. doi: 10.1016/j.frl.2020.101647 . [8] A. Ammy-Driss, M. Garcin, Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics, 2020. arXiv:2007.10727 . [9] R. Cerqueti, V. Ficcadenti, Anxiety for the pandemic and trust in financial markets, 2020. arXiv:2008.01649 . [10] M. Costola, M. Iacopini, C. R. M. A. Santagiustina, Public Concern and the Financial Markets during the COVID-19 outbreak, 2020. arXiv:2005.06796 . [11] M. Feldkircher, F. Huber, M. Pfarrhofer, Measuring the Effectiveness of US Monetary Policy during the COVID-19 Recession, 2020. arXiv:2007.15419 . [12] M. Garcin, J. Klein, S. Laaribi, Estimation of time-varying kernel densities and chronology of the impact of COVID-19 on financial markets, 2020. arXiv:2007.09043 . [13] M. Pagano, C. Wagner, J. Zechner, Disaster resilience and asset prices, 2020. arXiv:2005.08929 . [14] A. A. Toda, Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact, 2020. arXiv:2003.11221 . [15] S. Drożdż, J. Kwapień, P. Oświȩ, T. Stanisz, M. Wa̧ torek, Complexity in Economic and Social Systems: Cryptocurrency Market at around COVID-19, Entropy 22 (2020). doi: 10.3390/e22091043 . [16] R. K.-K. Pang, O. Granados, H. Chhajer, E. F. Legara, An analysis of network filtering methods to sovereign bond yields during COVID-19, 2021. arXiv:2009.13390 . [17] S. Semerikov, S. Chukharev, S. Sakhno, A. Striuk, V. Osadchyi, V. Solovieva, T. Vakaliuk, P. Nechypurenko, O. Bondarenko, H. Danylchuk, Our sustainable coronavirus future, E3S Web of Conferences 166 (2020). doi: 10.1051/e3sconf/202016600001 . [18] H. Danylchuk, L. Kibalnyk, O. Kovtun, A. Kiv, O. Pursky, G. Berezhna, Modelling of cryptocurrency market using fractal and entropy analysis in COVID-19, CEUR Workshop Proceedings 2713 (2020) 352–371. [19] A. Kaminskyi, M. Nehrey, N. Rizun, The impact of COVID-induced shock on the risk-return correspondence of agricultural ETFs, CEUR Workshop Proceedings 2713 (2020) 204–218. [20] N. Maksyshko, O. Vasylieva, I. Kozin, V. Perepelitsa, Comparative analysis of the attractiveness of investment instruments based on the analysis of market dynamics, CEUR Workshop Proceedings 2713 (2020) 219–238. [21] S. Semerikov, H. Kucherova, V. Los, D. Ocheretin, Neural network analytics and forecasting the country’s business climate in conditions of the coronavirus disease (COVID-19), CEUR Workshop Proceedings 2845 (2021) 22–32. [22] G. Malinetsky, Synergetics – from past to future, Modeling and Analysis of Information Systems 19 (2015) 5–31. doi: 10.18255/1818-1015-2012-3-5-31 . [23] V. Soloviev, N. Moiseienko, O. Tarasova, Modeling of cognitive process using complexity theory methods, CEUR Workshop Proceedings 2393 (2019) 905–918. [24] S. Somin, Y. Altshuler, G. Gordon, A. Pentland, E. Shmueli, Network dynamics of a financial ecosystem, Scientific Reports 10 (2020) 4587. doi: 10.1038/s41598-020-61346-y . [25] P. Grau, C. Jaureguizar, D. Jaureguizar, The cryptocurrency market: A network analysis, Esic Market Economics and Business Journal 49 (2018) 569–583. doi: 10.7200/esicm.161.0493.4i . [26] J. Liang, L. Li, D. Zeng, Evolutionary dynamics of cryptocurrency transaction networks: An empirical study, PLOS ONE 13 (2018) 1–18. doi: 10.1371/journal.pone.0202202 . [27] S. Thurner, P. Klimek, R. Hanel, Introduction to the theory of complex systems, Oxford University Press, Oxford, 2018. doi: 10.1093/oso/9780198821939.001.0001 . [28] S. Drożdż, L. Minati, P. Oświȩcimka, M. Stanuszek, M. Wa̧ torek, Competition of noise and collectivity in global cryptocurrency trading: Route to a self-contained market, Chaos: An Interdisciplinary Journal of Nonlinear Science 30 (2020) 023122. doi: 10.1063/1.5139634 . [29] M. Wa̧torek, S. Drożdż, J. Kwapień, L. Minati, P. Oświȩcimka, M. Stanuszek, Multiscale characteristics of the emerging global cryptocurrency market, Physics Reports 901 (2021) 1–82. doi: 10.1016/j.physrep.2020.10.005 . [30] A. O. Bielinskyi, I. Khvostina, A. Mamanazarov, A. Matviychuk, S. Semerikov, O. Serdyuk, V. Solovieva, V. N. Soloviev, Predictors of oil shocks. Econophysical approach in environmental science, IOP Conference Series: Earth and Environmental Science 628 (2021) 012019. doi: 10.1088/1755- 1315/628/1/012019 . [31] M. Ausloos, D. Grech, T. Di Matteo, R. Kutner, C. Schinckus, H. E. Stanley, Econophysics and sociophysics in turbulent world, Physica A: Statistical Mechanics and its Applications 531 (2020) 136–145. [32] W. B. Arthur, Foundations of complexity economics, Nature Reviews Physics 3 (2021) 136–145. doi: 10.1038/s42254-020-00273-3 . [33] R. Kutner, M. Ausloos, D. Grech, T. Di Matteo, C. Schinckus, H. Eugene Stanley, Econophysics and sociophysics: Their milestones & challenges, Physica A: Statistical Mechanics and its Applications 516 (2019) 240–253. doi: 10.1016/j.physa.2018.10.019 . [34] R. Mantegna, H. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance, volume 53, 2000. doi: 10.1063/1.1341926 . [35] A. Bielinskyi, O. Serdyuk, S. Semerikov, V. Soloviev, Econophysics of cryptocurrency crashes: an overview, SHS Web of Conferences 107 (2021) 03001. doi: 10.1051/shsconf/202110703001 . [36] Z.-Q. Jiang, W.-J. Xie, W.-X. Zhou, D. Sornette, Multifractal analysis of financial markets: a review, Reports on Progress in Physics 82 (2019) 125901. doi: 10.1088/1361-6633/ab42fb . [37] J. Kwapień, S. Drożdż, Physical approach to complex systems, Physics Reports 515 (2012) 115–226. doi: 10.1016/j.physrep.2012.01.007 , physical approach to complex systems. [38] B. E. Baaquie, Quantum Finance: Path Integrals and Hamiltonians for Options and Interest Rates, Cambridge University Press, 2004. [39] M. Schaden, Quantum finance, Physica A: Statistical Mechanics and its Applications 316 (2002) 511–538. doi: 10.1016/s0378- 4371(02)01200- 1 . [40] V. P. Maslov, V. E. Nazaikinskii, Mathematics underlying the 2008 financial crisis, and a possible remedy, 2009. arXiv:0811.4678 . [41] C. Schinckus, A methodological call for a quantum econophysics, in: Selected Papers of the 7th International Conference on Quantum Interaction - Volume 8369, QI 2013, Springer-Verlag, Berlin, Heidelberg, 2013, p. 308–316. doi: 10.1007/978-3-642-54943-4_28 . [42] V. Saptsin, V. Soloviev, Relativistic quantum econophysics - new paradigms in complex systems modelling, 2009. arXiv:0907.1142 . [43] V. Soloviev, V. Saptsin, Heisenberg uncertainty principle and economic analogues of basic physical quantities, 2011. arXiv:1111.5289 . [44] D. Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems, Princeton University Press, 2003. doi: doi:10.1515/9781400885091 . [45] Y. Peng, P. Albuquerque, J. Camboim de Sá, A. J. Padula, M. Montenegro, The best of two worlds: Forecasting High Frequency Volatility for cryptocurrencies and traditional currencies with Support Vector Regression, Expert Systems with Applications 97 (2017). doi: 10.1016/j.eswa.2017.12.004 . [46] Q. Zhao, A deep learning framework for predicting digital asset price movement from trade-by-trade data, 2020. arXiv:2010.07404 . [47] M. Amjad, D. Shah, Trading bitcoin and online time series prediction, in: O. Anava, A. Khaleghi, M. Cuturi, V. Kuznetsov, A. Rakhlin (Eds.), Proceedings of the Time Series Workshop at NIPS 2016, volume 55 of Proceedings of Machine Learning Research, PMLR, Barcelona, Spain, 2017, pp. 1–15. [48] T. Chen, C. Guestrin, XGBoost: A scalable Tree Boosting System, Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2016). doi: 10.1145/2939672.2939785 . [49] V. Derbentsev, A. Matviychuk, V. Soloviev, Forecasting of cryptocurrency prices using machine learning, in: L. Pichl, C. Eom, T. Kaizoji (Eds.), Advanced Studies of Financial Technologies and Cryptocurrency Markets, 1 ed., Springer, 2020, pp. 211–231. doi: 10.1007/978-981-15-4498-9_12 . [50] A. H. Dyhrberg, Bitcoin, gold and the dollar – a GARCH volatility analysis, Finance Research Letters 16 (2016) 85–92. [51] M. Ortu, N. Uras, C. Conversano, G. Destefanis, S. Bartolucci, On technical trading and social media indicators in cryptocurrencies’ price classification through deep learning, 2021. arXiv:2102.08189 . [52] N. Uras, L. Marchesi, M. Marchesi, R. Tonelli, Forecasting Bitcoin closing price series using linear regression and neural networks models, 2020. arXiv:2001.01127 . [53] A. Hachicha, F. Hachicha, Analysis of the bitcoin stock market indexes using comparative study of two models SV with MCMC algorithm, Review of Quantitative Finance and Accounting 56 (2021) 647–673. doi: 10.1007/s11156-020-00905-w . [54] J. Kaminski, Nowcasting the Bitcoin Market with Twitter Signals, 2016. arXiv:1406.7577 . [55] M. A. Kennis, Multi-channel discourse as an indicator for Bitcoin price and volume movements, 2018. arXiv:1811.03146 . [56] O. Kodama, L. Pichl, T. Kaizoji, Regime Change And Trend Prediction For Bitcoin Time Series Data, CBU International Conference Proceedings 5 (2017) 384–388. URL: https://ideas.repec.org/a/aad/iseicj/v5y2017i0p384-388.html. doi: 10.12955/cbup.v5.954 . [57] D. Shah, K. Zhang, Bayesian regression and Bitcoin, 2014. arXiv:1410.1231 . [58] V. Soloviev, S. V., Quantitative methods of estimation of complication are in prognostica- tion of the socio-economic systems, in: Modern problems of forecasting socio-economic processes: concepts, models, applied aspects, Tkachuk O. V., 2012, pp. 174–188. [59] M. Tarnopolski, Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach, 2017. arXiv:1707.03746 . [60] N. T. Courtois, M. Grajek, R. Naik, Optimizing sha256 in bitcoin mining, in: Z. Kotulski, B. Księżopolski, K. Mazur (Eds.), Cryptography and Security Systems, Springer Berlin Heidelberg, Berlin, Heidelberg, 2014, pp. 131–144. doi: 10.1007/978-3-662-44893-9_12 . [61] L. Kristoufek, Grandpa, Grandpa, Tell Me the One About Bitcoin Being a Safe Haven: New Evidence From the COVID-19 Pandemic, Frontiers in Physics 8 (2020). doi: 10.3389/fphy.2020.00296 . [62] D. Broomhead, G. P. King, Extracting qualitative dynamics from experimental data, Physica D: Nonlinear Phenomena 20 (1986) 217–236. doi: 10.1016/0167-2789(86)90031-X . [63] V. I. Ponomarenko, M. D. Prokhorov, Extracting information masked by the chaotic signal of a time-delay system, Phys. Rev. E 66 (2002) 026215. doi: 10.1103/PhysRevE.66.026215 . [64] M. Rajković, Extracting meaningful information from financial data, Physica A: Statistical Mechanics and its Applications 287 (2000) 383–395. doi: 10.1016/S0378-4371(00)00377-0 . [65] G. M. Caporale, L. A. Gil-Alana, A. Plastun, Persistence in the Cryptocurrency Market, CESifo Working Paper Series 6811, CESifo, 2017. URL: https://ideas.repec.org/p/ces/ceswps/_6811.html. [66] A. F. Bariviera, M. J. Basgall, W. Hasperué, M. Naiouf, Some stylized facts of the Bitcoin market, Physica A: Statistical Mechanics and its Applications 484 (2017) 82–90. doi: 10.1016/j.physa.2017.04.159 . [67] A. F. Bariviera, The inefficiency of Bitcoin revisited: A dynamic approach, Economics Letters 161 (2017) 1–4. doi: 10.1016/j.econlet.2017.09.013 . [68] J. Wang, G. Meric, Z. Liu, I. Meric, Stock market crashes, firm characteristics, and stock returns, Journal of Banking & Finance 33 (2009) 1563–1574. doi: 10.1016/j.jbankfin.2009.03.002 . [69] S. Lleo, W. T. Ziemba, Does the bond-stock earnings yield differential model predict equity market corrections better than high P/E models?, Financial Markets, Institutions & Instruments 26 (2017) 61–123. doi: 10.1111/fmii.12080 . [70] H. Hong, J. Stein, Differences of opinion, short-sales constraints, and market crashes, Review of Financial Studies 16 (2003) 487–525. [71] M. Shu, W. Zhu, Real-time prediction of Bitcoin bubble crashes, Physica A: Statistical Mechanics and its Applications 548 (2020) 124477. doi: 10.1016/j.physa.2020.124477 . [72] T. Klein, H. Pham Thu, T. Walther, Bitcoin is not the New Gold – A comparison of volatility, correlation, and portfolio performance, International Review of Financial Analysis 59 (2018) 105–116. doi: 10.1016/j.irfa.2018.07.010 . [73] K. Gkillas, F. Longin, Is Bitcoin the New Digital Gold? Evidence From Extreme Price Movements in Financial Markets, SSRN Electronic Journal (2019) 1–85. doi: 10.2139/ssrn.3245571 . [74] Y. Liu, A. Tsyvinski, X. Wu, Common Risk Factors in Cryptocurrency, NBER Working Papers 25882, National Bureau of Economic Research, Inc, 2019. [75] L. Kristoufek, What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis, PLOS ONE 10 (2015) 1–15. doi: 10.1371/journal.pone.0123923 . [76] X. Li, C. Wang, The technology and economic determinants of cryptocurrency exchange rates: The case of Bitcoin, Decision Support Systems 95 (2017) 49–60. doi: 10.1016/j.dss.2016.12.001 . [77] A. Bielinskyi, V. Soloviev, S. Semerikov, V. Solovieva, Detecting stock crashes using Levy distribution, CEUR Workshop Proceedings 2422 (2019) 420–433. [78] A. Bielinskyi, S. Semerikov, V. Solovieva, V. Soloviev, Levy ́s stable distribution for stock crash detecting, SHS Web Conf. 65 (2019) 06006. doi: 10.1051/shsconf/20196506006 . [79] V. Derbentsev, S. Semerikov, O. Serdyuk, V. Solovieva, V. Soloviev, Recurrence based entropies for sustainability indices, E3S Web of Conferences 166 (2020) 13031. doi: 10.1051/e3sconf/202016613031 . [80] V. N. Soloviev, A. Belinskiy, Complex systems theory and crashes of cryptocurrency market, in: V. Ermolayev, M. C. Suárez-Figueroa, V. Yakovyna, H. C. Mayr, M. Nikitchenko, A. Spivakovsky (Eds.), Information and Communication Technologies in Education, Research, and Industrial Applications, Springer International Publishing, Cham, 2019, pp. 276–297. doi: 10.1007/978-3-030-13929-2_14 . [81] V. Soloviev, A. Belinskiy, Methods of nonlinear dynamics and the construction of cryptocurrency crisis phenomena precursors, CEUR Workshop Proceedings 2104 (2018) 116–127. [82] V. Soloviev, A. Bielinskyi, O. Serdyuk, V. Solovieva, S. Semerikov, Lyapunov exponents as indicators of the stock market crashes, CEUR Workshop Proceedings 2732 (2020) 455–470. [83] V. Soloviev, S. Yevtushenko, V. Batareyev, Entropy analysis of crisis phenomena for DJIA index, CEUR Workshop Proceedings 2393 (2019) 434–449. [84] V. Soloviev, V. Solovieva, A. Tuliakova, M. Ivanova, Construction of crisis precursors in multiplex networks, in: Proceedings of the 2019 7th International Conference on Modeling, Development and Strategic Management of Economic System (MDSMES 2019), Atlantis Press, 2019/10, pp. 361–366. doi: 10.2991/mdsmes- 19.2019.68 . [85] V. Soloviev, O. Serdiuk, S. Semerikov, O. Kohut-Ferens, Recurrence entropy and financial crashes, in: Proceedings of the 2019 7th International Conference on Modeling, Development and Strategic Management of Economic System (MDSMES 2019), Atlantis Press, 2019/10, pp. 385–388. doi: 10.2991/mdsmes- 19.2019.73 . [86] V. Soloviev, A. Bielinskyi, N. Kharadzjan, Coverage of the coronavirus pandemic through entropy measures, CEUR Workshop Proceedings 2832 (2020) 24–42. [87] M. S. Kanwal, J. A. Grochow, N. Ay, Comparing Information-Theoretic Measures of Complexity in Boltzmann Machines, Entropy 19 (2017). URL: https://www.mdpi.com/1099-4300/19/7/310. doi: 10.3390/e19070310 . [88] D. Bonchev, Information theoretic complexity measures, in: R. A. Meyers (Ed.), Encyclopedia of Complexity and Systems Science, Springer, 2009, pp. 4820–4838. doi: 10.1007/978-0-387-30440-3_285 . [89] L. Lovász, Information and complexity (how to measure them?), The Emergence of Complexity in Mathematics, Physics, Chemistry and Biology, Pontifical Academy of Sciences (1996) 12. [90] L. T. Lui, G. Terrazas, H. Zenil, C. Alexander, N. Krasnogor, Complexity Measurement Based on Information Theory and Kolmogorov Complexity, Artificial Life 21 (2015) 205–224. doi: 10.1162/ARTL_a_00157 . [91] C. E. Shannon, A mathematical theory of communication, Bell System Technical Journal 27 (1948) 379–423. doi: 10.1002/j.1538- 7305.1948.tb01338.x . [92] G. Sommazzi, Kolmogorov Randomness, Complexity and the Laws of Nature, Bachelor in philosophy thesis, Università degli studi di Milano, 2016. URL: https://core.ac.uk/download/pdf/186331492.pdf. [93] J.-L. Blanc, L. Pezard, A. Lesne, Delay independence of mutual-information rate of two symbolic sequences, Phys. Rev. E 84 (2011) 036214. doi: 10.1103/PhysRevE.84.036214 . [94] S. Zozor, P. Ravier, O. Buttelli, On Lempel–Ziv complexity for multidimensional data analysis, Physica A: Statistical Mechanics and its Applications 345 (2005) 285–302. doi: 10.1016/j.physa.2004.07.025 . [95] E. Estevez-Rams, R. Lora Serrano, B. Aragón Fernández, I. Brito Reyes, On the non-randomness of maximum Lempel Ziv complexity sequences of finite size, Chaos: An Interdisciplinary Journal of Nonlinear Science 23 (2013) 023118. doi: 10.1063/1.4808251 . [96] S. D. Silva, R. Matsushita, R. Giglio, The relative efficiency of stockmarkets, Economics Bulletin 7 (2008) 1–12. [97] R. Giglio, R. Matsushita, A. Figueiredo, I. Gleria, S. D. Silva, Algorithmic complexity theory and the relative efficiency of financial markets, EPL (Europhysics Letters) 84 (2008) 48005. doi: 10.1209/0295-5075/84/48005 . [98] S. Da Silva, Financial Market Efficiency Should be Gauged in Relative Rather than Absolute Terms, MPRA Paper 64497, University Library of Munich, Germany, 2015. [99] S. Da Silva, C. Taufemback, R. Giglio, Algorithmic complexity theory detects decreases in the relative efficiency of stock markets in the aftermath of the 2008 financial crisis, Economics Bulletin 31 (2011) 1631–1647. [100] R. Giglio, S. Da Silva, Ranking the stocks listed on Bovespa according to their relative efficiency, MPRA Paper 22720, University Library of Munich, Germany, 2009. [101] A. Lempel, J. Ziv, On the complexity of finite sequences, IEEE Transactions on Information Theory 22 (1976) 75–81. doi: 10.1109/TIT.1976.1055501 . [102] O. Brandouy, J.-P. Delahaye, L. Ma, H. Zenil, Algorithmic complexity of financial motions, Research in International Business and Finance 30 (2014) 336–347. doi: 10.1016/j.ribaf.2012.08.001 . [103] P. Fiedor, Multiscale analysis of the predictability of stock returns, Risks 3 (2015) 219–233. doi: 10.3390/risks3020219 . [104] J. Gao, Y. Hou, F. Fan, F. Liu, Complexity Changes in the US and China’s Stock Markets: Differences, Causes, and Wider Social Implications, Entropy 22 (2020). URL: https://www.mdpi.com/1099-4300/22/1/75. doi: 10.3390/e22010075 . [105] H. Cao, Y. Li, Unraveling chaotic attractors by complex networks and measurements of stock market complexity, Chaos: An Interdisciplinary Journal of Nonlinear Science 24 (2014) 013134. doi: 10.1063/1.4868258 . [106] V. Soloviev, S. Semerikov, V. Solovieva, Lempel-Ziv Complexity and Crises of Cryptocurrency Market, in: Proceedings of the III International Scientific Congress Society of Ambient Intelligence 2020 (ISC-SAI 2020), Atlantis Press, 2020, pp. 299–306. doi: 10.2991/aebmr.k.200318.037 . [107] A. N. Kolmogorov, Three approaches to the quantitative definition of information, International Journal of Computer Mathematics 2 (1968) 157–168. doi: 10.1080/00207166808803030 . [108] M. Costa, C.-K. Peng, A. Goldberger, Multiscale analysis of heart rate dynamics: Entropy and time irreversibility measures, Cardiovascular engineering (Dordrecht, Netherlands) 8 (2008) 88–93. doi: 10.1007/s10558- 007- 9049- 1 . [109] R. Clausius, T. Hirst, The Mechanical Theory of Heat: With Its Applications to the Steam-Engine and to the Physical Properties of Bodies, Creative Media Partners, LLC, 2017. [110] L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen, volume 67, Vieweg+Teubner Verlag, 1970, pp. 115–225. doi: 10.1007/978-3-322-84986-1_3 . [111] J. W. Gibbs, Elementary principles in statistical mechanics developed with especial reference to the rational foundation of thermodynamics, C. Scribner, New York, 1902. [112] M. Vosvrda, J. Barunik, L. Vacha, M. Vošvrda, Tail Behavior of the Central European Stock Markets during the Financial Crisis, Czech Economic Review 4 (2010) 281–294. [113] J. S. Richman, J. R. Moorman, Physiological time-series analysis using approximate entropy and sample entropy, American Journal of Physiology-Heart and Circulatory Physiology 278 (2000) H2039–H2049. doi: 10.1152/ajpheart.2000.278.6.H2039 . [114] R. Sole, S. Valverde, Information Theory of Complex Networks: On Evolution and Architectural Constraints, volume 207, Springer, 2004, pp. 189–207. doi: 10.1007/978-3-540-44485-5_9 . [115] V. Soloviev, O. Serdiuk, The usage of Tsallis entropy for complexity evaluation in economic systems, in: Information technologies and modeling in economics: on the way to interdisciplinarity, Gate-Ukraine, 2013, pp. 115–129. [116] C. Tsallis, Introduction to nonextensive statistical mechanics: Approaching a complex world, Springer, 2009. doi: 10.1007/978- 0- 387- 85359- 8 . [117] A. Delgado-Bonal, A. Marshak, Approximate entropy and sample entropy: A comprehensive tutorial, Entropy 21 (2019). doi: 10.3390/e21060541 . [118] S. M. Pincus, Approximate entropy as a measure of system complexity, Proceedings of the National Academy of Sciences of the United States of America 88 (1991) 2297—2301. [119] S. M. Pincus, A. L. Goldberger, Physiological time-series analysis: what does regularity quantify?, American Journal of Physiology-Heart and Circulatory Physiology 266 (1994) H1643–H1656. doi: 10.1152/ajpheart.1994.266.4.H1643 . [120] K. Yun, H.-K. Park, D.-H. Kwon, Y.-T. Kim, S.-N. Cho, H.-J. Cho, B. S. Peterson, J. Jeong, Decreased cortical complexity in methamphetamine abusers, Psychiatry Research: Neuroimaging 201 (2012) 226–232. [121] S. N. Bhaduri, Applying Approximate Entropy (ApEn) to Speculative Bubble in the Stock Market, Journal of Emerging Market Finance 13 (2014) 43–68. doi: 10.1177/0972652714534023 . [122] C. Eom, G. Oh, W.-S. Jung, Relationship between efficiency and predictability in stock price change, Physica A: Statistical Mechanics and its Applications 387 (2008) 5511–5517. URL: https://ideas.repec.org/a/eee/phsmap/v387y2008i22p5511-5517.html. doi: 10.1016/j.physa.2008.05.0 . [123] S. Lahmiri, S. Bekiros, The impact of COVID-19 pandemic upon stability and sequential irregularity of equity and cryptocurrency markets, Chaos, Solitons & Fractals 138 (2020) 109936. doi: 10.1016/j.chaos.2020.109936 . [124] I. Mahmoud, K. Naoui, H. Jemmali, Study of speculative bubbles: The contribution of approximate entropy, International Journal of Economics and Financial Issues 3 (2013) 683–693. [125] S. Pincus, R. E. Kalman, Irregularity, volatility, risk, and financial market time series, Proceedings of the National Academy of Sciences 101 (2004) 13709–13714. [126] W.-Q. Duan, H. E. Stanley, Volatility, irregularity, and predictable degree of accumulative return series, Phys. Rev. E 81 (2010) 066116. doi: 10.1103/PhysRevE.81.066116 . [127] A. Delgado-Bonal, Quantifying the randomness of the stock markets, Sci. Rep. 9 (2019) 2045–2322. doi: 10.1038/s41598-019-49320-9 . [128] C. Bandt, B. Pompe, Permutation entropy: A natural complexity measure for time series, Phys. Rev. Lett. 88 (2002) 174102. URL: https://link.aps.org/doi/10.1103/PhysRevLett.88.174102. doi: 10.1103/PhysRevLett.88.174102 . [129] J. Amigó, Permutation Complexity in Dynamical Systems, Springer-Verlag Berlin Heidelberg, 2010. [130] M. Zanin, L. Zunino, O. A. Rosso, D. Papo, Permutation entropy and its main biomedical and econophysics applications: A review, Entropy 14 (2012) 1553–1577. [131] H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, 2 ed., Cambridge University Press, 2003. doi: 10.1017/CBO9780511755798 . [132] M. Henry, G. Judge, Permutation entropy and information recovery in nonlinear dynamic economic time series, Econometrics 7 (2019). doi: 10.3390/econometrics7010010 . [133] H. Sigaki, M. Perc, H. Ribeiro, Clustering patterns in efficiency and the coming-of-age of the cryptocurrency market, Scientific Reports 9 (2019). doi: 10.1038/s41598-018-37773-3 . [134] A. Sensoy, The inefficiency of Bitcoin revisited: A high-frequency analysis with alternative currencies, Finance Research Letters 28 (2019) 68–73. doi: 10.1016/j.frl.2018.04.002 . [135] A. Metin Karakaş, Entropy Approach for Volatility of Ethereum and Bitcoin, Asian Journal of Business and Management 7 (2019) 10–15. doi: 10.24203/ajbm.v7i1.5682 . [136] D. T. Pele, M. Mazurencu-Marinescu-Pele, Using high-frequency entropy to forecast bitcoin’s daily value at risk, Entropy 21 (2019). doi: 10.3390/e21020102 . [137] F. Takens, Detecting Strange Attractors in Turbulence, in: D. Rand, L.-S. Young (Eds.), Dynamical Systems and Turbulence, Warwick 1980, volume 898 of Lecture Notes in Mathematics, Springer, Berlin, 1981, pp. 366–381. doi: 10.1007/bfb0091924 . [138] J. P. Eckmann, D. Ruelle, Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57 (1985) 617–656. doi: 10.1103/RevModPhys.57.617 . [139] E. Ott, T. Sauer, J. Yorke, Coping with Chaos, Wiley Series in Nonlinear Science, Wiley, 1994. [140] C. L. Webber, Jr., J. P. Zbilut, Recurrence quantification analysis of nonlinear dynamical systems, in: M. A. Riley, G. C. V. Orden (Eds.), Tutorials in Contemporary Nonlinear Methods for the Behavioral Sciences, National Science Foundation (NSF), 2005, pp. 26–94. [141] R. Gu, Multiscale shannon entropy and its application in the stock market, Physica A: Statistical Mechanics and its Applications 484 (2017) 215–224. doi: 10.1016/j.physa.2017.04.164 . [142] B. B. Mandelbrot, J. A. Wheeler, The fractal geometry of nature, American Journal of Physics 51 (1983) 286–287. doi: 10.1119/1.13295 . [143] H. E. Hurst, Long-term storage capacity of reservoirs, Transactions of the American Society of Civil Engineers 116 (1951) 770–799. doi: 10.1061/TACEAT.0006518 . [144] H. E. Hurst, A suggested statistical model of some time series which occur in nature, Nature 180 (1957) 494. doi: 10.1038/180494a0 . [145] A. W. Lo, Long-term Memory in Stock Market Prices, Working Paper 2984, National Bureau of Economic Research, 1989. doi: 10.3386/w2984 . [146] C.-K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, A. L. Goldberger, Mosaic organization of DNA nucleotides, Phys. Rev. E 49 (1994) 1685–1689. [147] Z.-Q. Jiang, W.-J. Xie, W.-X. Zhou, Testing the weak-form efficiency of the WTI crude oil futures market, Physica A: Statistical Mechanics and its Applications 405 (2014) 235–244. doi: 10.1016/j.physa.2014.02.042 . [148] J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A: Statistical Mechanics and its Applications 316 (2002) 87–114. doi: 10.1016/s0378-4371(02)01383-3 . [149] F. Aslam, W. Mohti, P. Ferreira, Evidence of intraday multifractality in european stock markets during the recent coronavirus (COVID-19) outbreak, International Journal of Financial Studies 8 (2020). URL: https://www.mdpi.com/2227-7072/8/2/31. doi: 10.3390/ijfs8020031 . [150] R. Hasan, S. M. Mohammad, Multifractal analysis of Asian markets during 2007–2008 financial crisis, Physica A: Statistical Mechanics and its Applications 419 (2015) 746–761. doi: 10.1016/j.physa.2014.10.030 . [151] S. Kumar, N. Deo, Multifractal properties of the Indian financial market, Physica A: Statistical Mechanics and its Applications 388 (2009) 1593–1602. doi: 10.1016/j.physa.2008.12.0 . [152] J. Kwapień, P. Oświȩcimka, S. Drożdż, Components of multifractality in high-frequency stock returns, Physica A: Statistical Mechanics and its Applications 350 (2005) 466–474. [153] S. Lahmiri, Multifractal analysis of Moroccan family business stock returns, Physica A: Statistical Mechanics and its Applications 486 (2017) 183–191. doi: 10.1016/j.physa.1182017.05.048 . [154] J. W. Lee, K. Eun Lee, P. Arne Rikvold, Multifractal behavior of the Korean stock-market index KOSPI, Physica A: Statistical Mechanics and its Applications 364 (2006) 355–361. doi: 10.1016/j.physa.2005.08.082 . [155] K. Matia, Y. Ashkenazy, H. E. Stanley, Multifractal properties of price fluctuations of stocks and commodities, Europhysics Letters (EPL) 61 (2003) 422–428. doi: 10.1209/epl/i2003- 00194- y . [156] P. Suárez-García, D. Gómez-Ullate, Multifractality and long memory of a financial index, Physica A: Statistical Mechanics and its Applications 394 (2014) 226–234. doi: 10.1016/j.physa.2013.09.038 . [157] L. Zunino, A. Figliola, B. M. Tabak, D. G. Pérez, M. Garavaglia, O. A. Rosso, Multifractal structure in Latin-American market indices, Chaos, Solitons & Fractals 41 (2009) 2331–2340. doi: 10.1016/j.chaos.2008.09.013 . [158] F. Delbianco, F. Tohmé, T. Stosic, B. Stosic, Multifractal behavior of commodity markets: Fuel versus non-fuel products, Physica A: Statistical Mechanics and its Applications 457 (2016) 573–580. doi: 10.1016/j.physa.2016.03.096 . [159] R. Gu, H. Chen, Y. Wang, Multifractal analysis on international crude oil markets based on the multifractal detrended fluctuation analysis, Physica A: Statistical Mechanics and its Applications 389 (2010) 2805–2815. URL: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:14:p:2805-2815. [160] Z. Li, X. Lu, Multifractal analysis of China’s agricultural commodity futures markets, Energy Procedia 5 (2011) 1920–1926. doi: 10.1016/j.egypro.2011.03.330 , 2010 International Conference on Energy, Environment and Development - ICEED2010. [161] P. Mali, A. Mukhopadhyay, Multifractal characterization of gold market: A multifractal detrended fluctuation analysis, Physica A: Statistical Mechanics and its Applications 413 (2014) 361–372. doi: 10.1016/j.physa.2014.06.076 . [162] S. Zheng, X. Lan, Multifractal analysis of spot rates in tanker markets and their comparisons with crude oil markets, Physica A: Statistical Mechanics and its Applications 444 (2016) 547–559. [163] G. Lim, S. Kim, H. Lee, K. Kim, D.-I. Lee, Multifractal detrended fluctuation analysis of derivative and spot markets, Physica A: Statistical Mechanics and its Applications 386 (2007) 259–266. doi: 10.1016/j.physa.2007.07.055 . [164] P. Caraiani, E. Haven, Evidence of multifractality from CEE exchange rates against euro, Physica A Statistical Mechanics and its Applications 419 (2015) 395–407. doi: 10.1016/j.physa.2014.06.043 . [165] P. Norouzzadeh, B. Rahmani, A multifractal detrended fluctuation description of Iranian rial–US dollar exchange rate, Physica A: Statistical Mechanics and its Applications 367 (2006) 328–336. doi: 10.1016/j.physa.2005.11.019 . [166] G. Oh, C. Eom, S. Havlin, W.-S. Jung, F. Wang, H. Stanley, S. Kim, A multifractal analysis of Asian foreign exchange markets, Eur. Phys. J. B 85 (2012) 214. doi: 10.1140/epjb/e2012-20570-0 . [167] J. Qin, X. Lu, Y. Zhou, L. Qu, The effectiveness of China’s RMB exchange rate reforms: An insight from multifractal detrended fluctuation analysis, Physica A: Statistical Mechanics and its Applications 421 (2015) 443–454. doi: 10.1016/j.physa.2014.11.053 . [168] D.-H. Wang, X.-W. Yu, Y.-Y. Suo, Statistical properties of the yuan exchange rate index, Physica A: Statistical Mechanics and its Applications 391 (2012) 3503–3512. doi: 10.1016/j.physa.2012.01.054 . [169] P. Norouzzadeh, W. Dullaert, B. Rahmani, Anti-correlation and multifractal features of Spain electricity spot market, Physica A: Statistical Mechanics and its Applications 380 (2007) 333–342. doi: 10.1016/j.physa.2007.02.087 . [170] W. Mensi, A. K. Tiwari, S.-M. Yoon, Global financial crisis and weak-form efficiency of Islamic sectoral stock markets: An MF-DFA analysis, Physica A: Statistical Mechanics and its Applications 471 (2017) 135–146. doi: 10.1016/j.physa.2016.12.0 . [171] A. K. Tiwari, C. T. Albulescu, S.-M. Yoon, A multifractal detrended fluctuation analysis of financial market efficiency: Comparison using Dow Jones sector ETF indices, Physica A: Statistical Mechanics and its Applications 483 (2017) 182–192. doi: 10.1016/j.physa.2017.05.007 . [172] Y. Wang, Y. Wei, C. Wu, Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis, Physica A: Statistical Mechanics and its Applications 390 (2011) 817–827. doi: 10.1016/j.physa.2010.11.002 . [173] L. Zunino, B. Tabak, A. Figliola, D. Pérez, M. Garavaglia, O. Rosso, A multifractal approach for stock market inefficiency, Physica A: Statistical Mechanics and its Applications 387 (2008) 6558–6566. doi: 10.1016/j.physa.2008.08.028 . [174] B. Podobnik, H. E. Stanley, Detrended cross-correlation analysis: A new method for analyzing two nonstationary time series, Phys. Rev. Lett. 100 (2008) 084102. doi: 10.1103/PhysRevLett.100.084102 . [175] W.-X. Zhou, Multifractal detrended cross-correlation analysis for two nonstationary signals, Physical Review E 77 (2008). [176] N. Costa, C. Silva, P. Ferreira, Long-Range Behaviour and Correlation in DFA and DCCA Analysis of Cryptocurrencies, International Journal of Financial Studies 7 (2019). doi: 10.3390/ijfs7030051 . [177] X.-Y. Qian, Y.-M. Liu, Z.-Q. Jiang, B. Podobnik, W.-X. Zhou, H. E. Stanley, Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces, Phys. Rev. E 91 (2015) 062816. doi: 10.1103/PhysRevE.91.062816 . [178] Z.-Q. Jiang, W.-X. Zhou, Multifractal detrending moving-average cross-correlation analysis, Phys. Rev. E 84 (2011) 016106. doi: 10.1103/PhysRevE.84.016106 . [179] L. Kristoufek, Multifractal height cross-correlation analysis: A new method for analyzing long-range cross-correlations, EPL (Europhysics Letters) 95 (2011) 68001. doi: 10.1209/0295-5075/95/68001 . [180] J. Wang, P. Shang, W. Ge, Multifractal cross-correlation analysis based on statistical moments, Fractals 20 (2012) 271–279. doi: 10.1142/S0218348X12500259 . [181] J. Li, X. Lu, Y. Zhou, Cross-correlations between crude oil and exchange markets for selected oil rich economies, Physica A: Statistical Mechanics and its Applications 453 (2016) 131–143. URL: https://EconPapers.repec.org/RePEc:eee:phsmap:v:453:y:2016:i:c:p:131-143. [182] C. Xie, Y. Zhou, G. Wang, X. Yan, Analyzing the Cross-Correlation Between Onshore and Offshore RMB Exchange Rates Based on Multifractal Detrended Cross-Correlation Analysis (MF-DCCA), Fluctuation and Noise Letters 16 (2017) 1750004–226. doi: 10.1142/120S0219477517500043 . [183] F. Ma, Y. Wei, D. Huang, Multifractal detrended cross-correlation analysis between the Chinese stock market and surrounding stock markets, Physica A: Statistical Mechanics and its Applications 392 (2013) 1659–1670. [184] Y. Wang, Y. Wei, C. Wu, Cross-correlations between Chinese A-share and B-share markets, Physica A: Statistical Mechanics and its Applications 389 (2010) 5468–5478. doi: 10.1016/j.physa.2010.08.029 . [185] P. Yue, H.-C. Xu, W. Chen, X. Xiong, W.-X. Zhou, Liner and nonlinear correlations in the order aggressiveness of chinese stocks, Fractals 25 (2017) 1750041. [186] F. Ma, Y. Wei, D. Huang, L. Zhao, Cross-correlations between West Texas Intermediate crude oil and the stock markets of the BRIC, Physica A: Statistical Mechanics and its Applications 392 (2013) 5356–5368. [187] F. Ma, Q. Zhang, C. Peng, Y. Wei, Multifractal detrended cross-correlation analysis of the oil-dependent economies: Evidence from the West Texas intermediate crude oil and the GCC stock markets, Physica A: Statistical Mechanics and its Applications 410 (2014) 154–166. doi: 10.1016/j.physa.2014.05.023 . [188] Y. Wang, Y. Wei, C. Wu, Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil, Physica A: Statistical Mechanics and its Applications 390 (2011) 864–875. doi: 10.1016/j.physa.2010.11.017 . [189] X. Zhuang, Y. Wei, F. Ma, Multifractality, efficiency analysis of Chinese stock market and its cross-correlation with WTI crude oil price, Physica A: Statistical Mechanics and its Applications 430 (2015) 101–113. [190] X. Zhuang, Y. Wei, B. Zhang, Multifractal detrended cross-correlation analysis of carbon and crude oil markets, Physica A: Statistical Mechanics and its Applications 399 (2014) 113–125. doi: 10.1016/j.physa.2013.12.048 . [191] L. Xinsheng, L. Jianfeng, Z. Ying, Q. Yubo, Cross-correlations between RMB exchange rate and international commodity markets, Physica A: Statistical Mechanics and its Applications 486 (2017) 168–182. [192] Z. Zhang, Y. Zhang, D. Shen, W. Zhang, The dynamic cross-correlations between mass media news, new media news, and stock returns, Complexity 2018 (2018) 1–11. [193] Z. Zhang, Y. Zhang, D. Shen, W. Zhang, The cross-correlations between online sentiment proxies: Evidence from Google Trends and Twitter, Physica A: Statistical Mechanics and its Applications 508 (2018) 67–75. [194] Z. Da, J. Engelberg, P. Gao, The sum of all FEARS investor sentiment and asset prices, Review of Financial Studies 28 (2015) 1–32. doi: 10.1093/rfs/hhu072 . [195] W. Zhang, P. Wang, X. Li, D. Shen, Twitter’s daily happiness sentiment and international stock returns: Evidence from linear and nonlinear causality tests, Journal of Behavioral and Experimental Finance 18 (2018) 50–53. [196] M. Gronwald, C. Sattarhof, How to Measure Financial Market Efficiency?: A Multifractality-Based Quantitative Approach with an Application to the European Carbon Market, Working Paper 5, University of Aberdeen Business School, 2018. [197] T. Takaishi, Statistical properties and multifractality of Bitcoin, Physica A: Statistical Mechanics and its Applications 506 (2018) 507–519. doi: 10.1016/j.physa.2018.04.046 . [198] L. Kirichenko, V. Bulakh, T. Radivilova, Fractal time series analysis of social network activities, 2017 4th International Scientific-Practical Conference Problems of Infocommunications. Science and Technology (PIC S&T) (2017). doi: 10.1109/infocommst.2017.8246438 . [199] Y. Jiang, H. Nie, W. Ruan, Time-varying long-term memory in Bitcoin market, Finance Research Letters 25 (2018) 280–284. [200] A. Sensoy, E. Hacihasanoglu, Time-varying long range dependence in energy futures markets, Energy Economics 46 (2014) 318–327. doi: 10.1016/j.eneco.2014.09.023 . [201] K. H. Al-Yahyaee, W. Mensi, S.-M. Yoon, Efficiency, multifractality, and the long-memory property of the Bitcoin market: A comparative analysis with stock, currency, and gold markets, Finance Research Letters 27 (2018) 228–234. doi: 10.1016/j.frl.2018.03.017 . [202] G. Gajardo, W. D. Kristjanpoller, M. Minutolo, Does Bitcoin exhibit the same asymmetric multifractal cross-correlations with crude oil, gold and DJIA as the Euro, Great British Pound and Yen?, Chaos, Solitons & Fractals 109 (2018) 195–205. doi: 10.1016/j.chaos.2018.02.0 . [203] S. Lahmiri, S. Bekiros, A. Salvi, Long-range memory, distributional variation and randomness of bitcoin volatility, Chaos, Solitons & Fractals 107 (2018) 43–48. doi: 10.1016/j.chaos.2017.12.018 . [204] W. Zhang, P. Wang, X. Li, D. Shen, Multifractal Detrended Cross-Correlation Analysis of the Return-Volume Relationship of Bitcoin Market, Complexity 2018 (2018) 1–20. [205] A. Ganchuk, V. Derbentsev, V. Soloviev, Multifractal Properties of the Ukraine Stock Market, 2006. arXiv:physics/0608009v1 . [206] K. Hu, P. C. Ivanov, Z. Chen, P. Carpena, H. Eugene Stanley, Effect of trends on detrended fluctuation analysis, Phys. Rev. E 64 (2001) 011114. doi: 10.1103/PhysRevE.64.011114 . [207] Z. Chen, P. C. Ivanov, K. Hu, H. E. Stanley, Effect of nonstationarities on detrended fluctuation analysis, Phys. Rev. E 65 (2002) 041107. doi: 10.1103/PhysRevE.65.041107 . [208] J. R. Thompson, J. R. Wilson, Multifractal detrended fluctuation analysis: Practical applications to financial time series, Mathematics and Computers in Simulation 126 (2016) 63–88. doi: 10.1016/j.matcom.2016.03.003 . [209] D. Clark, L. Tarra, A. Berera, Chaos and information in two-dimensional turbulence, Phys. Rev. Fluids 5 (2020) 064608. doi: 10.1103/PhysRevFluids.5.064608 . [210] R. Engelken, F. Wolf, L. F. Abbott, Lyapunov spectra of chaotic recurrent neural networks, 2020. arXiv:2006.02427 . [211] K. Krishnamurthy, T. Can, D. J. Schwab, Theory of gating in recurrent neural networks, 2021. arXiv:2007.14823 . [212] W. S. Lee, S. Flach, Deep learning of chaos classification, 2020. arXiv:2004.10980 . [213] M. B. Tayel, E. I. AlSaba, Robust and sensitive method of Lyapunov exponent for heart rate variability, 2015. arXiv:1508.00996 . [214] H. De Thélin, T. Gauthier, G. Vigny, Parametric Lyapunov exponents, Bulletin of the London Mathematical Society (2020). doi: 10.1112/blms.12441 . [215] M. Cencini, F. Cecconi, A. Vulpiani, Chaos: From Simple Models to Complex Systems, volume 17 of Series on Advances in Statistical Mechanics, 2010. doi: 10.1142/7351 . [216] P. Grassberger, I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett. 50 (1983) 346–349. URL: https://link.aps.org/doi/10.1103/PhysRevLett.50.346. doi: 10.1103/PhysRevLett.50.346 . [217] J. C. Sprott, Chaos and Time-Series Analysis, Princeton University Press, 2001. [218] L.-S. Young, Mathematical theory of Lyapunov exponents, Journal of Physics A: Mathematical and Theoretical 46 (2013) 254001. [219] C. J. Gavilán-Moreno, G. Espinosa-Paredes, Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors, Nuclear Engineering and Technology 48 (2016) 434–447. doi: 10.1016/j.net.2016.01.002 . [220] A. Prieto-Guerrero, G. Espinosa-Paredes, Dynamics of BWRs and mathematical models, 2019, pp. 193–268. doi: 10.1016/B978-0-08-102445-4.00005-9 . [221] D. Nychka, S. Ellner, A. R. Gallant, D. McCaffrey, Finding chaos in noisy systems, Journal of the Royal Statistical Society: Series B (Methodological) 54 (1992) 399–426. [222] A. Wolf, J. Swift, H. L. Swinney, J. Vastano, Determining Lyapunov exponents from a time series, Physica D: Nonlinear Phenomena 16 (1985) 285 – 317. [223] M. Sano, Y. Sawada, Measurement of the Lyapunov spectrum from a chaotic time series, Phys. Rev. Lett. 55 (1985) 1082–1085. doi: 10.1103/PhysRevLett.55.1082 . [224] J. P. Eckmann, S. O. Kamphorst, D. Ruelle, S. Ciliberto, Liapunov exponents from time series, Phys. Rev. A 34 (1986) 4971–4979. doi: 10.1103/PhysRevA.34.4971 . [225] M. T. Rosenstein, J. J. Collins, C. J. De Luca, A practical method for calculating largest Lyapunov exponents from small data sets, Physica D: Nonlinear Phenomena 65 (1993) 117–134. doi: 10.1016/0167-2789(93)90009-P . [226] U. Parlitz, Identification of true and spurious Lyapunov exponents from time series, International Journal of Bifurcation and Chaos 02 (1992) 155–165. [227] M. Balcerzak, D. Pikunov, A. Dabrowski, The fastest, simplified method of Lyapunov exponents spectrum estimation for continuous-time dynamical systems, Nonlinear Dynamics 94 (2018) 3053–3065. doi: 10.1007/s11071-018-4544-z . [228] J. Gao, Y. Cao, W.-W. Tung, J. Hu, Multiscale Analysis of Complex Time Series: Integration of Chaos and Random Fractal Theory, and Beyond, Wiley, 2007. doi: 10.1002/9780470191651 . [229] J. Gao, J. Hu, W.-W. Tung, Y. Zheng, Multiscale analysis of economic time series by scale-dependent Lyapunov exponent, Quantitative Finance 13 (2013) 265–274. doi: 10.1080/14697688.2011.580774 . [230] V. Soloviev, D. Chabanenko, S. I., Using the scale-dependent Lyapunov exponent as a measure of complexity, in: M. Gedz (Ed.), The banking system of Ukraine in the context of globalization of financial markets: proceedings of VII International scientific and practical conference, CHIBS UBS NBU, 2012, pp. 469–471. [231] V. Soloviev, I. Stratiychuk, Use of indicator-precursors of crisis phenomena of the financial market on the basis of the scale-dependent Lyapunov exponent, The problems of economics 2 (2013) 279–283. [232] J.-P. Eckmann, S. O. Kamphorst, D. Ruelle, Recurrence plots of dynamical systems, Europhysics Letters (EPL) 4 (1987) 973–977. doi: 10.1209/0295-5075/4/9/004 . [233] J. Scheinkman, B. Lebaron, Nonlinear dynamics and stock returns, The Journal of Business 62 (1989) 311–37. [234] H. D. I. Abarbanel, R. Brown, J. J. Sidorowich, L. S. Tsimring, The analysis of observed chaotic data in physical systems, Rev. Mod. Phys. 65 (1993) 1331–1392. doi: 10.1103/RevModPhys.65.1331 . [235] V. S. Kulkarni, Complexity, chaos, and the duffing-oscillator model: An analysis of inventory fluctuations in markets, 2013. arXiv:1308.1616 . [236] O. Bajo-Rubio, F. Fernandez-Rodriguez, S. Sosvilla-Rivero, Chaotic behaviour in exchange-rate series : First results for the Peseta-U.S. dollar case, Economics Letters 39 (1992) 207–211. URL: https://ideas.repec.org/a/eee/ecolet/v39y1992i2p207-211.html. [237] W. D. Dechert, R. Gencay, Lyapunov exponents as a nonparametric diagnostic for stability analysis, Journal of Applied Econometrics 7 (1992) S41–S60. doi: 10.1002/jae.3950070505 . [238] R. Gençay, A statistical framework for testing chaotic dynamics via Lyapunov exponents, Physica D: Nonlinear Phenomena 89 (1996) 261–266. doi: 10.1016/0167-2789(95)00230-8 . [239] S. Shreemoyee, C. Vikhyat, Analysing the behaviour of local hurst exponent and Lyapunov exponent for prediction of market crashes, Engineering and Technology International Journal of Economics and Management Engineering 13 (2019). [240] S. Srinivasan, S. Prasad, S. Patil, G. Lazarou, J. Picone, Estimation of Lyapunov spectra from a time series, in: Proceedings of the IEEE SoutheastCon 2006, 2006, pp. 192–195. doi: 10.1109/second.2006.1629348 . [241] L. Mastroeni, P. Vellucci, ”Chaos” in energy and commodity markets: a controversial matter, 2017. arXiv:1611.07432 . [242] V. Plakandaras, R. Gupta, M. E. Wohar, Persistence of economic uncertainty: a comprehensive analysis, Applied Economics 51 (2019) 4477–4498. doi: 10.1080/00036846.2019.1591607 . [243] G. Chakrabarti, C. Sen, Anatomy of Global Stock Market Crashes, number 978-81-322-0463-3 in SpringerBriefs in Economics, Springer, 2012. doi: 10.1007/978-81-322-0463-3 . [244] J. Liesen, V. Mehrmann, Linear Algebra, Springer Undergraduate Mathematics Series, 1 ed., Springer, 2015. [245] C. Touzé, A. Chaigne, Lyapunov exponents from experimental time series. Application to cymbal vibrations, Acustica 86 (2000) 1–36. [246] B. Podobnik, A. Valentinčič, D. Horvatić, H. E. Stanley, Asymmetric Lévy flight in financial ratios, Proceedings of the National Academy of Sciences of the United States of America 108 (2011) 17883—17888. doi: 10.1073/pnas.1113330108 . [247] L. Bachelier, Théorie de la spéculation, Annales scientifiques de l’École Normale Supérieure 3e série, 17 (1900) 21–86. URL: http://www.numdam.org/item/ASENS_1900_3_17__21_0/. doi: 10.24033/asens.476 . [248] X. Gabaix, P. Gopikrishnan, V. Plerou, H. Stanley, A theory of power-law distributions in financial market fluctuations, Nature 423 (2003) 267–70. doi: 10.1038/nature01624 . [249] M. Kateregga, S. Mataramvura, D. Taylor, Parameter estimation for stable distributions with application to commodity futures log-returns, Cogent Economics & Finance 5 (2017) 1318813. doi: 10.1080/23322039.2017.1318813 . [250] D. Krężołek, The application of alpha-stable distributions in portfolio selection problem – the case of metal market, Studia Ekonomiczne 247 (2015) 57–68. [251] T. Lux, D. Sornette, On rational bubbles and fat tails, Journal of Money, Credit and Banking 34 (2002) 589–610. [252] Y. Malevergne, V. Pisarenko, D. Sornette, Empirical distributions of stock returns: between the stretched exponential and the power law?, Quantitative Finance 5 (2005) 379–401. doi: 10.1080/14697680500151343 . [253] Y. Malevergne, V. Pisarenko, D. Sornette, Testing the Pareto against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities, Phys. Rev. E 83 (2011) 036111. doi: 10.1103/PhysRevE.83.036111 . [254] N. N. Taleb, On the statistical differences between binary forecasts and real-world payoffs, International Journal of Forecasting 36 (2020) 1228–1240. doi: 10.1016/j.ijforecast.2019.12.004 . [255] N. N. Taleb, Y. Bar-Yam, P. Cirillo, On single point forecasts for fat-tailed variables, 2020. arXiv:2007.16096 . [256] P. Gopikrishnan, M. Meyer, L. Amaral, H. Stanley, Inverse cubic law for the distribution of stock price variations, The European Physical Journal B 3 (1998) 139–140. doi: 10.1007/s100510050292 . [257] P. Gopikrishnan, V. Plerou, L. A. Nunes Amaral, M. Meyer, H. E. Stanley, Scaling of the distribution of fluctuations of financial market indices, Phys. Rev. E 60 (1999) 5305–5316. doi: 10.1103/PhysRevE.60.5305 . [258] B. Podobnik, D. Horvatic, A. M. Petersen, H. E. Stanley, Cross-correlations between volume change and price change, Proceedings of the National Academy of Sciences of the United States of America 106 (2009) 22079—22084. doi: 10.1073/pnas.0911983106 . [259] B. Podobnik, K. Matia, A. Chessa, P. C. Ivanov, Y. Lee, H. E. Stanley, Time evolution of stochastic processes with correlations in the variance: stability in power-law tails of distributions, Physica A Statistical Mechanics and its Applications 300 (2001) 300–309. doi: 10.1016/S0378- 4371(01)00390- 9 . [260] X. Gabaix, Power laws in economics and finance, Annual Review of Economics 1 (2009) 255–294. doi: 10.1146/annurev.economics.050708.142940 . [261] Z. Kostanjčar, B. Jeren, Emergence of power-law and two-phase behavior in financial market fluctuations, Advances in Complex Systems 16 (2013) 1350008. doi: 10.1142/S0219525913500082 . [262] A. Chakraborty, S. Easwaran, S. Sinha, Deviations from universality in the fluctuation behavior of a heterogeneous complex system reveal intrinsic properties of components: The case of the international currency market, 2018. arXiv:1606.06111 . [263] T. Takaishi, Recent scaling properties of bitcoin price returns, 2020. arXiv:2009.06874 . [264] S. Drożdż, R. Gȩbarowski, L. Minati, P. Oświȩcimka, M. Waa̧ torek, Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects, Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (2018) 071101. doi: 10.1063/1.5036517 . [265] T. Takaishi, Time-varying properties of asymmetric volatility and multifractality in Bitcoin, PLOS ONE 16 (2021) e0246209. doi: 10.1371/journal.pone.0246209 . [266] S. Begušić, Z. Kostanjčar, H. Eugene Stanley, B. Podobnik, Scaling properties of extreme price fluctuations in Bitcoin markets, Physica A: Statistical Mechanics and its Applications 510 (2018) 400–406. doi: 10.1016/j.physa.2018.06.1 . [267] B. Mandelbrot, The variation of certain speculative prices, The Journal of Business 36 (1963). [268] P. Levy, Théorie des erreurs. La loi de Gauss et les lois exceptionnelles, Bulletin de la Société Mathématique de France 52 (1924) 49–85. doi: 10.24033/bsmf.1046 . [269] B. Mandelbrot, The Pareto-Lévy Law and the Distribution of Income, International Economic Review 1 (1960) 79–106. [270] E. S. Andersen, Mathematica Scandinavica 3 (1955) 185–187. URL: http://www.jstor.org/stable/24490356. [271] I. A. Koutrouvelis, Regression-type estimation of the parameters of stable laws, Journal of the American Statistical Association 75 (1980) 918–928. doi: 10.1080/01621459.1980.10477573 . [272] B. Brorsen, S. Yang, Maximum likelihood estimates of symmetric stable distribution parameters, Communications in Statistics Part B: Simulation and Computation 19 (1990) 1459–1464. doi: 10.1080/03610919008812928 . [273] J. Nolan, Maximum Likelihood Estimation and Diagnostics for Stable Distributions, Birkhäuser, Boston, MA, 2001, pp. 379–400. doi: 10.1007/978-1-4612-0197-7_17 . [274] E. F. Fama, R. Roll, Parameter estimates for symmetric stable distributions, Journal of the American Statistical Association 66 (1971) 331–338. doi: 10.1080/01621459.1971.10482264 . [275] J. H. McCulloch, Simple consistent estimators of stable distribution parameters, Communications in Statistics - Simulation and Computation 15 (1986) 1109–1136. doi: 10.1080/03610918608812563 . [276] X. Ma, C. L. Nikias, Parameter estimation and blind channel identification in impulsive signal environments, IEEE Transactions on Signal Processing 43 (1995) 2884–2897. doi: 10.1109/78.476432 . [277] M. Shao, C. L. Nikias, Signal processing with fractional lower order moments: stable processes and their applications, Proceedings of the IEEE 81 (1993) 986–1010. doi: 10.1109/5.231338 . [278] J.-M. Nicolas, 1 - Introduction aux Statistiques de deuxiéme espéce : applications des Logs-moments et des Logs-cumulants á l’analyse des lois d’images radar, Traitement Du Signal 19 (2002) 139–167. [279] E. E. Kuruoglu, Density parameter estimation of skewed α-stable distributions, IEEE Transactions on Signal Processing 49 (2001) 2192–2201. doi: 10.1109/78.950775 . [280] W. H. DuMouchel, On the Asymptotic Normality of the Maximum-Likelihood Estimate when Sampling from a Stable Distribution, The Annals of Statistics 1 (1973) 948 – 957. doi: 10.1214/aos/1176342516 . [281] V. M. Zolotarev, One-dimensional stable distributions, volume 65 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, 1986. Translated from the Russian by H. H. McFaden, Translation edited by Ben Silver. [282] J. M. Chambers, C. L. Mallows, B. W. Stuck, A method for simulating stable random variables, Journal of the American Statistical Association 71 (1976) 340–344. URL: http://www.jstor.org/stable/2285309. [283] S. Bianchi, A. Pantanella, Pointwise regularity exponents and well-behaved residuals in stock markets, International Journal of Trade, Economics and Finance 2 (2011) 52–60. doi: 10.7763/IJTEF.2011.V2.78 . [284] V. I. Arnold, A. Avez, Ergodic problems of classical mechanics, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 50 (1970) 506–506. doi: 10.1002/zamm.19700500721 . [285] K. Umeno, Ergodic transformations on R preserving Cauchy laws, Nonlinear Theory and Its Applications, IEICE 7 (2016) 14–20. doi: 10.1587/nolta.7.14 . [286] I. A. Koutrouvelis, An iterative procedure for the estimation of the parameters of stable laws, Communications in Statistics - Simulation and Computation 10 (1981) 17–28. doi: 10.1080/03610918108812189 . [287] V. Soloviev, V. Solovieva, D. Chabanenko, Dynamics of α-stable Levy process parameters for returns distribution of the financial time series, in: O. Chernyak, P. Zakharchenko (Eds.), Contemporary concepts of forecasting the development of complex socio-economic systems, FO-P Tkachuk O V, Berdyansk, 2014, pp. 257–264. [288] H. Poincaré, The Three-Body Problem and the Equations of Dynamics, Astrophysics and Space Science Library, 1 ed., Springer, Cham, 2017. doi: 10.1007/978-3-319-52899-1 . [289] P. Faure, H. Korn, A new method to estimate the Kolmogorov entropy from recurrence plots: its application to neuronal signals, Physica D: Nonlinear Phenomena 122 (1998) 265–279. doi: 10.1016/S0167-2789(98)00177-8 . [290] M. Thiel, M. C. Romano, J. Kurths, Analytical description of recurrence plots of white noise and chaotic processes, Applied Nonlinear Dynamics 11 (2003). [291] M. Thiel, M. Romano, J. Kurths, R. Meucci, E. Allaria, F. Arecchi, Influence of observational noise on the recurrence quantification analysis, Physica D: Nonlinear Phenomena 171 (2002) 138–152. doi: 10.1016/S0167- 2789(02)00586- 9 . [292] L. Charles, J. Webber, I. Cornel, M. Norbert (Eds.), Recurrence Plots and Their Quantifications: Expanding Horizons, volume 180 of Springer Proceedings in Physics, Springer, 2015. doi: 10.1007/978-3-319-29922-8 . [293] N. Marwan, M. Carmen Romano, M. Thiel, J. Kurths, Recurrence plots for the analysis of complex systems, Physics Reports 438 (2007) 237–329. doi: 10.1016/j.physrep.2006.11.001 . [294] G. Jianbo, C. Huaqing, On the structures and quantification of recurrence plots, Physics Letters A 270 (2000) 75–87. doi: 10.1016/S0375-9601(00)00304-2 . [295] N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Recurrence-plot-based measures of complexity and their application to heart-rate-variability data, Phys. Rev. E 66 (2002) 026702. doi: 10.1103/PhysRevE.66.026702 . [296] C. L. Webber, J. P. Zbilut, Dynamical assessment of physiological systems and states using recurrence plot strategies, Journal of Applied Physiology 76 (1994) 965–973. doi: 10.1152/jappl.1994.76.2.965 . [297] J. P. Zbilut, C. L. Webber, Embeddings and delays as derived from quantification of recurrence plots, Physics Letters A 171 (1992) 199–203. [298] G. Corso, T. L. Prado, G. Z. dos S. Lima, S. R. Lopes, A novel entropy recurrence quantification analysis, 2017. arXiv:1707.00944 . [299] M. A. Little, P. E. McSharry, S. J. Roberts, D. A. Costello, I. M. Moroz, Exploiting nonlinear recurrence and fractal scaling properties for voice disorder detection, BioMedical Engineering OnLine 6 (2007) 23. doi: 10.1186/1475- 925x- 6- 23 . [300] H. Rabarimanantsoa, L. Achour, C. Letellier, A. Cuvelier, J.-F. Muir, Recurrence plots and Shannon entropy for a dynamical analysis of asynchronisms in noninvasive mechanical ventilation, Chaos: An Interdisciplinary Journal of Nonlinear Science 17 (2007) 013115. doi: 10.1063/1.2435307 . [301] S. R. Lopes, T. L. Prado, G. Corso, G. Z. dos S. Lima, J. Kurths, Parameter-free quantification of stochastic and chaotic signals, Chaos, Solitons & Fractals 133 (2020) 109616. doi: 10.1016/j.chaos.2020.109616 . [302] A. L. Goldberger, L. A. N. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov, R. G. Mark, J. E. Mietus, G. B. Moody, C.-K. Peng, H. E. Stanley, PhysioBank, PhysioToolkit, and PhysioNet, Circulation 101 (2000) e215–e220. doi: 10.1161/01.CIR.101.23.e215 . [303] M. Kirchner, P. Schubert, M. Liebherr, C. T. Haas, Detrended Fluctuation Analysis and Adaptive Fractal Analysis of Stride Time Data in Parkinson’s Disease: Stitching Together Short Gait Trials, PLOS ONE 9 (2014) 1–6. doi: 10.1371/journal.pone.0085787 . [304] I. Prigogine, From Being to Becoming Time and Complexity in the Physical Sciences, 1 ed., W.H. Freeman & Co, 1981. [305] M. Costa, A. L. Goldberger, C.-K. Peng, Multiscale entropy analysis of biological signals, Phys. Rev. E 71 (2005) 021906. doi: 10.1103/PhysRevE.71.021906 . [306] V. Soloviev, O. Rybchinska, Quantitative method of estimating the length of the recession according to the irreversibility of stock indices, Bulletin of the Kryvyi Rih Economic Institute KEI 2 (2010) 52–56. [307] S. Daw, C. Finney, M. Kennel, Symbolic approach for measuring temporal ”irreversibility”, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 62 (2000) 1912–21. doi: 10.1103/PhysRevE.62.1912 . [308] C. Diks, J. C. van Houwelingen, F. Takens, J. DeGoede, Reversibility as a criterion for discriminating time series, Physics Letters A 201 (1995) 221–228. doi: 10.1016/0375-9601(95)00239-Y . [309] J. F.Donges, R. V. Donner, J. Kurths, Testing time series irreversibility using complex network methods, EPL (Europhysics Letters) 102 (2013) 10004. doi: 10.1209/0295-5075/102/10004 . [310] P. Guzik, J. Piskorski, T. Krauze, A. Wykretowicz, H. Wysocki, Heart rate asymmetry by Poincaré plots of RR intervals, Biomedizinische Technik. Biomedical engineering 51 (2006) 272–5. doi: 10.1515/BMT.2006.054 . [311] M. B. Kennel, Testing time symmetry in time series using data compression dictionaries, Phys. Rev. E 69 (2004) 056208. URL: https://link.aps.org/doi/10.1103/PhysRevE.69.056208. doi: 10.1103/PhysRevE.69.056208 . [312] L. Lacasa, A. Nuñez, E. Roldán, J. M. R. Parrondo, B. Luque, Time series irreversibility: a visibility graph approach, The European Physical Journal B 85 (2012). doi: 10.1140/epjb/e2012-20809-8 . [313] A. Porta, S. Guzzetti, N. Montano, T. Gnecchi-Ruscone, R. Furlan, A. Malliani, Time reversibility in short-term heart period variability, in: Computers in Cardiology, volume 33, 2006, pp. 77–80. 2006 Computers in Cardiology, CIC ; Conference date: 17-09-2006 Through 20-09-2006. [314] M. Zanin, A. Rodríguez-González, E. Menasalvas Ruiz, D. Papo, Assessing time series reversibility through permutation patterns, Entropy 20 (2018). doi: 10.3390/e20090665 . [315] W. Yao, W. Yao, D. Yao, D. Guo, J. Wang, Shannon entropy and quantitative time irreversibility for different and even contradictory aspects of complex systems, Applied Physics Letters 116 (2020) 014101. doi: 10.1063/1.5133419 . [316] J. Li, P. Shang, X. Zhang, Time series irreversibility analysis using Jensen–Shannon divergence calculated by permutation pattern, Nonlinear Dynamics 96 (2019) 2637–2652. [317] R. Flanagan, L. Lacasa, Irreversibility of financial time series: A graph-theoretical approach, Physics Letters A 380 (2016) 1689–1697. doi: 10.1016/j.physleta.2016.03.011 . [318] J.-A. Martín-Gonzalo, I. Pulido-Valdeolivas, Y. Wang, T. Wang, G. Chiclana-Actis, M. d. C. Algarra-Lucas, I. Palmí-Cortés, J. Fernández Travieso, M. D. Torrecillas-Narváez, A. A. Miralles-Martinez, E. Rausell, D. Gómez-Andrés, M. Zanin, Permutation Entropy and Irreversibility in Gait Kinematic Time Series from Patients with Mild Cognitive Decline and Early Alzheimer’s Dementia, Entropy 21 (2019) 868. doi: 10.3390/e21090868 . [319] J. H. Martínez, J. L. Herrera-Diestra, M. Chavez, Detection of time reversibility in time series by ordinal patterns analysis, Chaos: An Interdisciplinary Journal of Nonlinear Science 28 (2018) 123111. doi: 10.1063/1.5055855 . [320] Y. Wenpo, J. Dai, M. Perc, J. Wang, D. Yao, D. Guo, Permutation-based time irreversibility in epileptic electroencephalograms, Nonlinear Dynamics 100 (2020) 907–919. doi: 10.1007/s11071-020-05506-9 . [321] W. Yao, W. Yao, J. Wang, Equal heartbeat intervals and their effects on the nonlinearity of permutation-based time irreversibility in heart rate, Physics Letters A 383 (2019) 1764–1771. doi: 10.1016/j.physleta.2019.03.002 . [322] G. G. Malinetsky, Theory of self-organization. on the cusp of IV paradigm, Computer research and modeling 5 (2013) 315–366. doi: 10.20537/2076-7633-2013-5-3-315-336 . [323] T. U. Grund, Dynamical Processes on Complex Networks (4th ed.) by A. Barrat, M. Barthélemy, & A. Vespignani, The Journal of Mathematical Sociology 37 (2013) 131–132. doi: 10.1080/0022250X.2012.728886 . [324] R. Cohen, S. Havlin, Complex Networks: Structure, Robustness and Function, Cambridge University Press, 2010. doi: 10.1017/CBO9780511780356 . [325] G. Bianconi, Interdisciplinary and physics challenges of network theory, EPL (Europhysics Letters) 111 (2015) 56001. doi: 10.1209/0295- 5075/111/56001 . [326] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Complex networks: Structure and dynamics, Physics Reports 424 (2006) 175–308. doi: 10.1016/j.physrep.2005.10.009 . [327] H. B. Danilchuk, V. N. Soloviev, Dynamics of graph spectral entropy in financial crisis, in: Socio-Economic Aspects of Economics and Managment, Aspekt Publishing of Budget Printing Cente, 2015, pp. 227–234. [328] V. Soloviev, Network measures of complexity of socio-economic systems, Bulletin of Cherkasy University 38 (2015) 67–79. [329] V. Soloviev, V. Solovieva, A. Tuliakova, Visibility graphs and precursors of stock crashes, Neuro-Fuzzy Modeling Techniques in Economics 8 (2019) 3–29. doi: 10.33111/nfmte.2019.003 . [330] V. Soloviev, V. Solovieva, A. Tuliakova, A. Hostryk, L. Pichl, Complex networks theory and precursors of financial crashes, CEUR Workshop Proceedings 2713 (2020) 53–67. [331] S. Boccaletti, G. Bianconi, R. Criado, C. del Genio, J. Gómez-Gardeñes, M. Romance, I. Sendiña-Nadal, Z. Wang, M. Zanin, The structure and dynamics of multilayer networks, Physics Reports 544 (2014) 1–122. doi: 10.1016/j.physrep.2014.07.001 , the structure and dynamics of multilayer networks. [332] M.-C. Qian, Z.-Q. Jiang, W.-X. Zhou, Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices, Journal of Physics A: Mathematical and Theoretical 43 (2010) 335002. doi: 10.1088/1751- 8113/43/33/335002 . [333] J. L. Birch, Modelling Financial Markets using Methods from Network Theory, Ph.D. thesis, University of Liverpool, 2015. [334] F. Liu, N. Wang, D. Wei, Analysis of chinese stock market by using the method of visibility graph, The Open Cybernetics & Systemics Journal 11 (2017) 36–43. doi: 10.2174/1874110X01711010036 . [335] W. Yan, E. van Tuyll van Serooskerken, Forecasting financial extremes: A network degree measure of super-exponential growth, PLOS ONE 10 (2015) 1–15. doi: 10.1371/journal.pone.0128908 . [336] A. Johansen, O. Ledoit, D. Sornette, Crashes as critical points, International Journal of Theoretical and Applied Finance 03 (2000) 219–255. doi: 10.1142/S0219024900000115 . [337] M. D. Vamvakaris, A. A. Pantelous, K. M. Zuev, Time series analysis of S&P 500 index: A horizontal visibility graph approach, Physica A: Statistical Mechanics and its Applications 497 (2018) 41–51. doi: 10.1016/j.physa.2018.01.010 . [338] M. Serafino, A. Gabrielli, G. Caldarelli, G. Cimini, Statistical validation of financial time series via visibility graph, 2017. arXiv:1710.10980 . [339] C. Coquidé, J. Lages, D. L. Shepelyansky, Contagion in bitcoin networks, Lecture Notes in Business Information Processing (2019) 208–219. doi: 10.1007/978-3-030-36691-9_18 . [340] T. Squartini, A. Gabrielli, D. Garlaschelli, T. Gili, A. Bifone, F. Caccioli, Complexity in neural and financial systems: From time-series to networks, Complexity 2018 (2018) 1–2. doi: 10.1155/2018/3132940 . [341] L. Lacasa, V. Nicosia, V. Latora, Network structure of multivariate time series, Scientific Reports 5 (2015). doi: 10.1038/srep15508 . [342] L. Bargigli, G. di Iasio, L. Infante, F. Lillo, F. Pierobon, The multiplex structure of interbank networks, Quantitative Finance 15 (2015) 673–691. doi: 10.1080/14697688.2014.968356 . [343] S. Li, S. Wen, Multiplex Networks of the Guarantee Market: Evidence from China, Complexity 2017 (2017) 1–7. doi: 10.1155/2017/9781890 . [344] C. Stephen, Dynamic phase and group detection in pedestrian crowd data using multiplex visibility graphs, Procedia Computer Science 53 (2015) 410–419. doi: 10.1016/j.procs.2015.07.318 . [345] R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, J. Kurths, Recurrence-based time series analysis by means of complex network methods, International Journal of Bifurcation and Chaos 21 (2011) 1019–1046. doi: 10.1142/S0218127411029021 . [346] L. Lacasa, B. Luque, F. Ballesteros, J. Luque, J. C. Nuño, From time series to complex networks: The visibility graph, Proceedings of the National Academy of Sciences 105 (2008) 4972–4975. doi: 10.1073/pnas.0709247105 . [347] V. Soloviev, A. Tuliakova, Graphodynamical methods for studying the complexity of modern stock markets, Neuro-fuzzy modeling technologies in economics 5 (2016) 152–179. [348] J. Iacovacci, L. Lacasa, Sequential motif profile of natural visibility graphs, Physical Review E 94 (2016). doi: 10.1103/physreve.94.052309 . [349] A. de la Concha, S. Martinez-Jaramillo, C. Carmona, Multiplex Financial Networks: Revealing the Level of Interconnectedness in the Banking System, in: Complex Networks & Their Applications VI, Springer International Publishing, 2018, pp. 1135–1148. doi: 10.1007/978-3-319-72150-7_92 . [350] G. Colangelo, F. M. Ciurana, L. C. Bianchet, R. J. Sewell, M. W. Mitchell, Simultaneous tracking of spin angle and amplitude beyond classical limits, Nature 543 (2017) 525–528. doi: 10.1038/nature21434 . [351] E. G. Hidalgo, Quantum econophysics, 2006. arXiv:physics/0609245 . [352] V. P. Maslov, Econophysics and quantum statistics, Math. Notes 72 (2002) 811–818. doi: 10.1023/A:1021489913179 . [353] V. Soloviev, O. Serdiuk, Quantum econophysical precursors of cryptocurrency crashes, Bulletin of Cherkasy University 1 (2009) 3–16. doi: 10.31651/2076-5886-2019-1-3-16 . [354] E. Benítez Rodríguez, L. Aguilar, Disturbance-disturbance uncertainty relation: The statistical distinguishability of quantum states determines disturbance, Scientific Reports 8 (2018) 4010. doi: 10.1038/s41598- 018- 22336- 3 . [355] L. A. Rozema, A. Darabi, D. H. Mahler, A. Hayat, Y. Soudagar, A. M. Steinberg, Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements, Phys. Rev. Lett. 109 (2012) 100404. doi: 10.1103/PhysRevLett.109.100404 . [356] M. Berta, M. Christandl, R. Colbeck, J. M. Renes, R. Renner, The uncertainty principle in the presence of quantum memory, Nature Physics 6 (2010) 659–662. doi: 10.1038/nphys1734 . [357] R. Prevedel, D. R. Hamel, R. Colbeck, K. Fisher, K. J. Resch, Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement, Nature Physics 7 (2011) 757–761. doi: 10.1038/nphys2048 . [358] L. Landau, E. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Course of Theoretical Physics, 3 ed., Butterworth-Heinemann, 1981. [359] V. Soloviev, Y. Romanenko, Economic analog of Heisenberg uncertainly principle and financial crisis, in: System analysis and information technology : 19-th International conference, SAIT 2017, ESC ”IASA” NTUU ”Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine, 2017, pp. 32–33. [360] V. Soloviev, S. Yevtushenko, V. Batareyev, Comparative analysis of the cryptocurrency and the stock markets using the Random Matrix Theory, CEUR Workshop Proceedings 2546 (2019) 87–100. [361] S. Drozdz, J. Kwapien, P. Oswiecimka, Empirics versus RMT in financial cross-correlations, 2007. arXiv:0711.0644 . [362] F. J. Dyson, Statistical Theory of the Energy Levels of Complex Systems. I, Journal of Mathematical Physics 3 (1962) 140–156. doi: 10.1063/1.1703773 . [363] E. P. Wigner, On a class of analytic functions from the quantum theory of collisions, Annals of Mathematics 53 (1951) 36–67. [364] P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109 (1958) 1492–1505. URL: https://link.aps.org/doi/10.1103/PhysRev.109.1492. doi: 10.1103/PhysRev.109.1492 . [365] A. Lipton, A. Sardon, F. Schär, C. Schüpbach, From tether to libra: Stablecoins, digital currency and the future of money, 2020. arXiv:2005.12949 . [366] C. Karmakar, A. Khandoker, J. Gubbi, M. Palaniswami, Modified Ehlers’ index for improved detection of heart rate asymmetry in Poincaré plot, in: 36th Annual Computers in Cardiology Conference (CinC), volume 36, IEEE, 2009, pp. 169 – 172. [367] A. Porta, S. Guzzetti, N. Montano, T. Gnecchi-Ruscone, R. Furlan, A. Malliani, Time reversibility in short-term heart period variability, in: 2006 Computers in Cardiology, volume 2006, IEEE, 2006, pp. 77 – 80. [368] A. Puglisi, D. Villamaina, Irreversible effects of memory, EPL 88 (2009) 30004. doi: 10.1209/0295-5075/88/30004 . [369] A. Abhishta, R. Joosten, S. Dragomiretskiy, L. Nieuwenhuis, Impact of Successful DDoS Attacks on a Major Crypto-Currency Exchange, in: 2019 27th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP), IEEE, United States, 2019, pp. 379–384. doi: 10.1109/EMPDP.2019.8671642 . [370] A. A. Kochkarov, S. D. Osipovich, R. A. Kochkarov, Analysis of DDoS Attacks on Bitcoin Cryptocurrency Payment System, Revista ESPACIOS 41 (2020) 29. [371] M. Conti, E. Sandeep Kumar, C. Lal, S. Ruj, A Survey on Security and Privacy Issues of Bitcoin, IEEE Communications Surveys & Tutorials 20 (2018) 3416–3452. doi: 10.1109/comst.2018.2842460 . [372] M. Mirkin, Y. Ji, J. Pang, A. Klages-Mundt, I. Eyal, A. Juels, BDoS: Blockchain Denial of Service, 2020. arXiv:1912.07497 . [373] M. Vasek, M. Thornton, T. Moore, Empirical Analysis of Denial-of-Service Attacks in the Bitcoin Ecosystem, in: R. Böhme, M. Brenner, T. Moore, M. Smith (Eds.), Financial Cryptography and Data Security. FC 2014. Lecture Notes in Computer Science, volume 8438 of FC 2014, Springer, 2014, pp. 57–71. doi: 10.1007/978-3-662-44774-1_5 . [374] U. Hacioglu (Ed.), Blockchain Economics and Financial Market Innovation, Contributions to Economics, 1 ed., Springer, 2019. doi: 10.1007/978-3-030-25275-5 . [375] S. Nakamoto, Bitcoin: A peer-to-peer electronic cash system, 2009. URL: http://www.bitcoin.org/bitcoin.pdf. [376] D. Aggarwal, G. Brennen, T. Lee, M. Santha, M. Tomamichel, Quantum attacks on bitcoin, and how to protect against them, Ledger 3 (2018). doi: 10.5195/ledger.2018.127 . [377] D. Sapaev, D. Bulychkov, F. Ablayev, A. Vasiliev, M. Ziatdinov, Quantum-assisted blockchain, 2018. arXiv:1802.06763 . [378] O. Sattath, On the insecurity of quantum Bitcoin mining, International Journal of Information Security 19 (2020) 291–302. doi: 10.1007/s10207-020-00493-9 . [379] L. Tessler, T. Byrnes, Bitcoin and quantum computing, 2018. arXiv:1711.04235 . [380] L. Alessandretti, A. ElBahrawy, L. M. Aiello, A. Baronchelli, Anticipating cryptocurrency prices using machine learning, Complexity 2018 (2018) 1–16. doi: 10.1155/2018/8983590 . [381] N. Gandal, H. Halaburda, Can We Predict the Winner in a Market with Network Effects? Competition in Cryptocurrency Market, Games 7 (2016). doi: 10.3390/g7030016 . [382] T. Guo, A. Bifet, N. Antulov-Fantulin, Bitcoin volatility forecasting with a glimpse into buy and sell orders, 2018 IEEE International Conference on Data Mining (ICDM) (2018). doi: 10.1109/icdm.2018.00123 . [383] H. Jang, J. Lee, An Empirical Study on Modeling and Prediction of Bitcoin Prices With Bayesian Neural Networks Based on Blockchain Information, IEEE Access 6 (2018) 5427–5437. doi: 10.1109/ACCESS.2017.2779181 . [384] O. Sattarov, A. Muminov, C. W. Lee, H. K. Kang, R. Oh, J. Ahn, H. J. Oh, H. S. Jeon, Recommending cryptocurrency trading points with deep reinforcement learning approach, Applied Sciences 10 (2020). doi: 10.3390/app10041506 . [385] D. Zhao, A. Rinaldo, C. Brookins, Cryptocurrency price prediction and trading strategies using support vector machines, 2019. arXiv:1911.11819 . [386] T. R. Li, A. S. Chamrajnagar, X. R. Fong, N. R. Rizik, F. Fu, Sentiment-based prediction of alternative cryptocurrency price fluctuations using gradient boosting tree model, Frontiers in Physics 7 (2019) 98. doi: 10.3389/fphy.2019.00098 . [387] W. Wei, Q. Zhang, L. Liu, Bitcoin transaction forecasting with deep network representation learning, 2020. arXiv:2007.07993 . [388] A. H. A. Othman, S. Kassim, R. B. Rosman, N. H. B. Redzuan, Prediction accuracy improvement for Bitcoin market prices based on symmetric volatility information using artificial neural network approach, Journal of Revenue and Pricing Management 19 (2020) 314–330. URL: https://ideas.repec.org/a/pal/jorapm/v19y2020i5d10.1057_s41272-020-00229-3.html. doi: 10.1057/s41272-020-00229- . [389] S. McNally, J. Roche, S. Caton, Predicting the price of bitcoin using machine learning, in: 2018 26th Euromicro International Conference on Parallel, Distributed and Network-based Processing (PDP), 2018, pp. 339–343. doi: 10.1109/PDP2018.2018.00060 . [390] S. M. Raju, A. M. Tarif, Real-Time Prediction of BITCOIN Price using Machine Learning Techniques and Public Sentiment Analysis, 2020. arXiv:2006.14473 . [391] Y. Hua, Bitcoin price prediction using ARIMA and LSTM, E3S Web Conf. 218 (2020) 01050. doi: 10.1051/e3sconf/202021801050 .
URI (Уніфікований ідентифікатор ресурсу): https://ceur-ws.org/Vol-3048/paper03.pdf
http://elibrary.kdpu.edu.ua/xmlui/handle/123456789/6974
https://doi.org/10.31812/123456789/6974
ISSN: 1613-0073
Розташовується у зібраннях:Кафедра інформатики та прикладної математики

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