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Solanum mauritianum hairs Universality on markets Ryszard Kutner Faculty of Physics, University of Warsaw, Poland Econophysics Network – Inaugural Workshop School of Business, University of Leicester Leicester UK, 10th October 2016 [1] J. Ludescher and A. Bunde, Phys. Rev. E 90, 062809 (2014). [2] J. Ludescher, C. Tsallis, A. Bunde, Eur. Phys. Lett. 95, 68002 (2011). [3] M. I. Bogachev and Bunde, Phys. Rev. E 80, 026131 (2009). [4] M. I. Bogachev and A. Bunde, Phys. Rev. E 78, 036114 (2008). [5] A. Corral, Physica A 340, 590 (2004). [6] M. Denys, M. Jagielski, T. Gubiec, R. Kutner, H.E. Stanley, Phys. Rev. E 94, 042305 (2016). 25-years of Rosario N. Mantegna paper: `Lévy walk and Enhanced Diffusion in Milan Stock Exchange', Physica A 179, 232 (1991). He empirically proved that the Central Limit Theorem is broken on the Milan Stock Exchange. That is, the Bachelier paradigm was broken. It inspired the avalanche of papers. In fact, it was the beginning of modern econophysics (although this name was introduced later). Generic goal Presentation of a novel (advanced) way of the non-Gaussian time series classification Schedule Motivation (1) Definiton of the problem and generic goal: inspiration from geophysics. (2) Extended the Gutenberg-Richter law (Earthquakes) for financial markets. (3) Superstatistics of excessive losses: empirical data colapse. (4) Superscaling (5) Concluding remarks: (i) excessive profits, (ii) risk estimation, and (ii) weighted superstatistics for Earthquakes. (1) Definition of the problem and a goal Our goal is to describe a universal behaviour of empirical statistics: (i) of interoccurrence (interevent) times between excessive losses and separately (ii) the excessive profits, as well as (iii) of interevent times between Earthquakes having amplitude above some threshold (defined by the Richter scale). Three basic concepts in study of excessive losses, ecessive profits, and Earthquakes: - activity - threshold - universality (1) Definition of the problem and a goal Two concrete related problems caused by empirical data of Ludescher, Bogachev, Tsallis, and Bunde arise: (i) Finding of probability of losses greater or equal than some threshold value vs. threshold value Q (e.g., VaR approach is a special case); (ii) Finding of probability distribution of intervent times ΔQt between successive excessive losses for various values of the threshold (basic distribution of the Continuous-time Random Walk). (1) Definition of the problem and a goal What is the statistics of excessive losses? Market seismograph measures Marketquakes. (Figures taken from [2]) (2) Extended the Gutenberg-Richter law for Earthquakes Jan. 2000 – June 2010: USD/GBP, S&P 500, IBM, WTI (crude oil) Subsequent inspiration from geophysics. Econo(geo)physics: main distribution Mean conditional discrete time period (3) Superstatistics vs. empirical data colapse Parameters of the superstatistics (for the IBM) Appendix: Particular cases (4) Superscaling. Final goal: (5) Concluding remarks: (i) Excessive profits Functional (not literal) balance between losses and profits. (5) Concluding remarks: (ii) Risk estimation: dynamical VaR. Zipf law for long-time limit (5) Concluding remarks: (iii) Weighted superstatistics vs. Earthquakes (5) Concluding remarks: Criticality Market activity, measured by the length of interevent time, has multiscale character. This activity defines a hierarchy of long interevent times as their distribution constitutes (asymptotically) a power-law. This means that slowly vanishing memory is present in the system. Hence, the system as a whole participates in this vanishing. Therefore, we can suppose that system is controlled by large fluctuations and long-range dependences. System is dominated by critical behaviour. There is also dependence between interevent times. Universality (data colapse) of this distribution is observed. The challenge. M. Jagielski, R.Kutner, and D. Sornette Which class of fractional stochastic dynamic equation leads to our solution? Which class of fractional kinetic equations produces our solution? Which class of agent-based models gives our waiting-time distributions so good fitted to empirical data? The challenge. (Figure taken from [1]) Thank you very much for your attention