DSpace Home
→
Електронні публікації
→
Фізико-математичний факультет
→
Кафедра інформатики та прикладної математики
→
View Item

Comparative analysis of the cryptocurrency and the stock markets using the Random Matrix Theory

Соловйов, Володимир Миколайович; Yevtushenko, Symon P.; Batareyev, Viktor V.

URI: http://elibrary.kdpu.edu.ua/xmlui/handle/123456789/3681
https://doi.org/10.31812/123456789/3681

Date: 2020-02-09

Abstract:

This article demonstrates the comparative possibility of constructing indicators of critical and crash phenomena in the volatile market of cryptocurrency and developed stock market. Then, combining the empirical cross-correlation matrix with the Random Matrix Theory, we mainly examine the statistical properties of cross-correlation coefficients, the evolution of the distribution of eigenvalues and corresponding eigenvectors in both markets using the daily returns of price time series. 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 introduced the largest eigenvalue of the matrix of correlations can act like indicators-predictors of falls in both markets.

Description:

1. Albert, R., Barabási, A.-L.: Statistical Mechanics of Complex Networks. Rev. Mod. Phys. 74, 47–97 (2002). doi:10.1103/RevModPhys.74.47 2. Albuquerque, Y., 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 Systems With Applications 97, 177–192. (2018) https://doi.org/10.1016/j.eswa.2017.12.004 3. Alessandretti, L., ElBahrawy, A., Aiello, L.M., Baronchelli, A.: Machine Learning the Cryptocurrency Market. https://ssrn.com/abstract=3183792 (2018). doi:10.2139/ssrn.3183792. Accessed 15 Sep 2018 4. Anderson, P.W.: Absence of Diffusion in Certain Random Lattices. Phys. Rev. 109(5), 1492–1505 (1958). doi:10.1103/PhysRev.109.1492 5. Andrews, B., Calder, M., Davis, R.A.: Maximum Likelihood Estimation for α-Stable Autoregressive Processes. The Annals of Statistics 37(4), 1946–1982 (2009). doi:10.1214/08-AOS632 6. Bielinskyi, A., Soloviev, V., Semerikov, S., Solovieva, V.: Detecting Stock Crashes Using Levy Distribution. In: Kiv, A., Semerikov, S., Soloviev, V., Kibalnyk, L., Danylchuk, H., Matviychuk, A. (eds.) Experimental Economics and Machine Learning for Prediction of Emergent Economy Dynamics, Proceedings of the Selected Papers of the 8th International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2 2019), Odessa, Ukraine, May 22-24, 2019. CEUR Workshop Proceedings 2422, 420–433. http://ceur-ws.org/Vol-2422/paper34.pdf (2019). Accessed 1 Aug 2019 7. Chen, T., Guestrin, C.: XGBoost: A Scalable Tree Boosting System. In: KDD '16 Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, August 13-17, 2016, pp. 785-794 (2016). doi:10.1145/2939672.2939785 8. Dassios, A., Li, L.: An Economic Bubble Model and Its First Passage Time. arXiv:1803.08160v1 [q-fin.MF]. https://arxiv.org/pdf/1803.08160.pdf (2018). Accessed 21 Mar 2019 9. Dyson, F.J.: Statistical Theory of the Energy Levels of Complex Systems. Journal of Mathematical Physics 3, 140–156 (1962). doi:10.1063/1.1703773 10. Guo, T., Antulov-Fantulin, N.: An experimental study of Bitcoin fluctuation using machine learning methods. arXiv:1802.04065v2 [stat.ML]. https://arxiv.org/pdf/1802.04065.pdf (2018). Accessed 25 Oct 2018 11. Halvin, S., Cohen, R.: Complex networks. Structure, robustness and function. Cambridge University Press, New York (2010) 12. Jiang, S., Guo, J., Yang, C., Tian, L.: Random Matrix Analysis of Cross-correlation in Energy Market of Shanxi, China. International Journal of Nonlinear Science 23(2), 96–101. http://www.internonlinearscience.org/upload/papers/IJNS%20Vol%2023%20%20No%20 2%20Paper%206-%20Random%20Matrix.pdf (2017). Accessed 25 Oct 2019 13. Kennis, M.A.: Multi-channel discourse as an indicator for Bitcoin price and volume movements. arXiv:1811.03146v1 [q-fin.ST]. https://arxiv.org/pdf/1811.03146.pdf (2018). Accessed 25 Oct 2019 14. Kiv, A., Semerikov, S., Soloviev, V., Kibalnyk, L., Danylchuk, H., Matviychuk, A.: Experimental Economics and Machine Learning for Prediction of Emergent Economy Dynamics. In: Kiv, A., Semerikov, S., Soloviev, V., Kibalnyk, L., Danylchuk, H., Matviychuk, A. (eds.) Experimental Economics and Machine Learning for Prediction of Emergent Economy Dynamics, Proceedings of the Selected Papers of the 8th International Conference on Monitoring, Modeling & Management of Emergent Economy (M3E2 2019), Odessa, Ukraine, May 22-24, 2019. CEUR Workshop Proceedings 2422, 1–4. http://ceurws.org/Vol-2422/paper00.pdf (2019). Accessed 1 Aug 2019 15. Kodama, O., Pichl, L., Kaizoji, T.: Regime Change and Trend Prediction for Bitcoin Time Series Data. In: Hájek P., Vít O., Bašová P., Krijt M., Paszeková H., Součková O., Mudřík R. (eds.) CBU International Proceedings 2017: Innovations in Science and Education, Prague, 22–24 March 2017, pp. 384–388. Central Bohemia University Prague (2017). doi:10.12955/cbup.v5.954 16. Laloux, L., Cizeau, P., Bouchaud, J.-P., Potters, M.: Noise dressing of financial correlation matrices. Physical Review Letters 83(7), 1467–1470 (1999). doi:10.1103/PhysRevLett.83.1467 17. Mantegna, R.N., Stanley, H.E.: An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge University Press, Cambridge (2000) 18. Mehta, L.M.: Random Matrices, 3 rd edn. Academic Press, San Diego (2004) 19. Newman, M., Barabási A.-L., Watts D.J. (eds.): The Structure and Dynamics of Networks. Princeton University Press, Princeton and Oxford (2006) 20. Newman, M.E.J.: The Structure and Function of Complex Networks. SIAM Reviews 45(2), 167–256 (2003). doi:10.1137/S003614450342480 21. Nikolis, G., Prigogine, I.: Exploring Complexity: An Introduction. St. Martin’s Press, New York (1989) 22. Pharasi, H.K., Sharma, K., Chakraborti, A., Seligman, T.H.: Complex Market Dynamics in the Light of Random Matrix Theory. In: Abergel F., Chakrabarti B., Chakraborti A., Deo N., Sharma K. (eds.) New Perspectives and Challenges in Econophysics and Sociophysics, pp. 13–34. New Economic Windows. Springer, Cham (2019). doi:10.1007/978-3-030- 11364-3_2 23. 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) 24. Saptsin, V., Soloviev, V.: Relativistic quantum econophysics – new paradigms in complex systems modelling. arXiv:0907.1142v1 [physics.soc-ph]. https://arxiv.org/pdf/0907.1142.pdf (2009). Accessed 25 Oct 2019 25. Shah, D., Zhang, K.: Bayesian regression and Bitcoin. In: 2014 52nd Annual Allerton Conference on Communication, Control, and Computing (Allerton), Monticello, 30 Sept. – 3 Oct. 2014. IEEE (2014). doi:10.1109/ALLERTON.2014.7028484 26. Shen, J., Zheng, B.: Cross-correlation in financial dynamics. EPL (Europhysics Letters) 86(4), 48005 (2009). doi:10.1209/0295-5075/86/48005 27. Soloviev, V., Belinskij, A.: Methods of nonlinear dynamics and the construction of cryptocurrency crisis phenomena precursors. In: Ermolayev, V., Suárez-Figueroa, M.C., Yakovyna, V., Kharchenko, V., Kobets, V., Kravtsov, H., Peschanenko, V., Prytula, Y., Nikitchenko, M., Spivakovsky, A. (eds.) Proceedings of the 14th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, Kyiv, Ukraine, May 14-17, 2018. CEUR Workshop Proceedings 2014, 116–127. http://ceur-ws.org/Vol-2104/paper_175.pdf (2018). Accessed 25 Oct 2019 28. Soloviev, V., Moiseienko, N., Tarasova, O.: Modeling of cognitive process using complexity theory methods. In: Ermolayev V., Mallet F., Yakovyna V., Kharchenko V., Kobets V., Korniłowicz A., Kravtsov H., Nikitchenko M., Semerikov S., Spivakovsky A. (eds.) Proceedings of the 15th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II Workshops. Kherson, Ukraine, June 12-15, 2019. CEUR Workshop Proceedings, vol. 2393, pp. 905–918. http://ceur-ws.org/Vol-2393/paper_356.pdf (2019). Accessed 25 Oct 2019 29. Soloviev, V., Serdiuk, O., Semerikov, S., Kohut-Ferens, O.: Recurrence entropy and financial crashes. In: Horal L., Soloviev V., Matviychuk A., Khvostina I. (eds.). Proceedings of the 2019 7th International Conference on Modeling, Development and Strategic Management of Economic System (MDSMES 2019). Advances in Economics, Business and Management Research, vol. 99, pp. 385–388. Atlantis Press, Paris (2019). doi:10.2991/mdsmes-19.2019.73 30. Soloviev, V., Solovieva, V., Tuliakova, A., Ivanova, M.: Construction of crisis precursors in multiplex networks. In: Horal L., Soloviev V., Matviychuk A., Khvostina I. (eds.). Proceedings of the 2019 7th International Conference on Modeling, Development and Strategic Management of Economic System (MDSMES 2019). Advances in Economics, Business and Management Research, vol. 99, pp. 361–366. Atlantis Press, Paris (2019). doi:10.2991/mdsmes-19.2019.68 31. Soloviev, V.N., Belinskiy, A.: 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 (14th International Conference, ICTERI 2018, Kyiv, Ukraine, May 14-17, 2018, Revised Selected Papers). Communications in Computer and Information Science, vol. 1007, pp. 276-297. Springer, Cham (2019). doi:10.1007/978-3- 030-13929-2_14 32. Song J.Y., Chang W., Song J.W.: Cluster analysis on the structure of the cryptocurrency market via Bitcoin-Ethereum filtering. Physica A: Statistical Mechanics and its Applications 527, 121339 (2019). doi:10.1016/j.physa.2019.121339 33. Stosic, Darco, Stosic, Dusan, Ludermir, T.B., Stosic, T.: Collective behavior of cryptocurrency price changes. Physica A: Statistical Mechanics and its Applications 507, 499–509 (2018). doi:10.1016/j.physa.2018.05.050 34. Tarnopolski, M.: Modeling the price of Bitcoin with geometric fractional Brownian motion: a Monte Carlo approach. arXiv:1707.03746v3 [q-fin.CP]. https://arxiv.org/pdf/1707.03746.pdf (2017). Accessed 17 Aug 2019 35. Urama, T.C., Ezepue, P.O., Nnanwa, C.P.: Analysis of Cross-Correlations in Emerging Markets Using Random Matrix Theory. Journal of Mathematical Finance 7(2), 291–307 (2017). doi:10.4236/jmf.2017.72015 36. Wang, M., Zhao, L., Du, R., Wang, C., Chen, L., Tian, L., Stanley, H.E.: A novel hybrid method of forecasting crude oil prices using complex network science and artificial intelligence algorithms. Applied Energy 220, 480–495 (2018). doi:10.1016/j.apenergy.2018.03.148 37. Wigner, E.P.: On a class of analytic functions from the quantum theory of collisions. Annals of Mathematics Second Series 53(1), 36–67 (1951). doi:10.2307/1969342

Show full item record