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Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework

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  • Potirakis, Stelios M.
  • Zitis, Pavlos I.
  • Eftaxias, Konstantinos

Abstract

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and the dynamics of economic (financial) systems can be analyzed within similar mathematical frameworks. We apply concepts of the nonextensive statistical physics, on time-series data of observable manifestations of the underlying complex processes ending up with these different extreme events, in order to support the suggestion that a dynamical analogy exists between a financial crisis (in the form of share or index price collapse) and a single earthquake. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg–Richter distribution of event sizes). We show that the populations of: (i) fracto-electromagnetic events rooted in the activation of a single fault, emerging prior to a significant earthquake, (ii) the trade volume events of different shares/economic indices, prior to a collapse, and (iii) the price fluctuation (considered as the difference of maximum minus minimum price within a day) events of different shares/economic indices, prior to a collapse, follow both the traditional Gutenberg–Richter law as well as a nonextensive model for earthquake dynamics, with similar parameter values. The obtained results imply the existence of a dynamic analogy between earthquakes and economic crises, which moreover follow the dynamics of seizures, magnetic storms and solar flares.

Suggested Citation

  • Potirakis, Stelios M. & Zitis, Pavlos I. & Eftaxias, Konstantinos, 2013. "Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2940-2954.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:13:p:2940-2954
    DOI: 10.1016/j.physa.2013.03.006
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    as
    1. Balasis, Georgios & Daglis, Ioannis A. & Anastasiadis, Anastasios & Papadimitriou, Constantinos & Mandea, Mioara & Eftaxias, Konstantinos, 2011. "Universality in solar flare, magnetic storm and earthquake dynamics using Tsallis statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 341-346.
    2. H. E. Stanley & V. Plerou, 2001. "Scaling and universality in economics: empirical results and theoretical interpretation," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 563-567.
    3. S. Potirakis & G. Minadakis & K. Eftaxias, 2012. "Sudden drop of fractal dimension of electromagnetic emissions recorded prior to significant earthquake," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 64(1), pages 641-650, October.
    4. Eftaxias, Konstantinos & Minadakis, George & Potirakis, Stelios. M. & Balasis, Georgios, 2013. "Dynamical analogy between epileptic seizures and seismogenic electromagnetic emissions by means of nonextensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(3), pages 497-509.
    5. D. Sornette, 2003. "Critical Market Crashes," Papers cond-mat/0301543, arXiv.org.
    6. Michael C. Munnix & Takashi Shimada & Rudi Schafer & Francois Leyvraz Thomas H. Seligman & Thomas Guhr & H. E. Stanley, 2012. "Identifying States of a Financial Market," Papers 1202.1623, arXiv.org.
    7. Bhattacharyya, Pratip & Chatterjee, Arnab & Chakrabarti, Bikas K., 2007. "A common mode of origin of power laws in models of market and earthquake," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 377-382.
    8. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    9. Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Papers cond-mat/0204331, arXiv.org, revised Sep 2002.
    10. Stanley, H.Eugene, 2003. "Statistical physics and economic fluctuations: do outliers exist?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(1), pages 279-292.
    11. Vilar, C.S. & França, G.S. & Silva, R. & Alcaniz, J.S., 2007. "Nonextensivity in geological faults?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 285-290.
    12. Potirakis, S.M. & Minadakis, G. & Eftaxias, K., 2012. "Analysis of electromagnetic pre-seismic emissions using Fisher information and Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 300-306.
    13. Zunino, L. & Pérez, D.G. & Kowalski, A. & Martín, M.T. & Garavaglia, M. & Plastino, A. & Rosso, O.A., 2008. "Fractional Brownian motion, fractional Gaussian noise, and Tsallis permutation entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6057-6068.
    14. Garas, Antonios & Argyrakis, Panos, 2007. "Correlation study of the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 399-410.
    15. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    16. J. C. Ferrero, 2011. "An statistical analysis of stratification and inequity in the income distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 80(2), pages 255-261, March.
    17. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.
    18. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    19. Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
    20. S. M.D. Queirós & C. Tsallis, 2005. "On the connection between financial processes with stochastic volatility and nonextensive statistical mechanics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 48(1), pages 139-148, November.
    21. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    22. Carpinteri, A. & Lacidogna, G. & Niccolini, G., 2009. "Fractal analysis of damage detected in concrete structural elements under loading," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2047-2056.
    23. Eftaxias, K., 2010. "Footprints of nonextensive Tsallis statistics, selfaffinity and universality in the preparation of the L’Aquila earthquake hidden in a pre-seismic EM emission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 133-140.
    24. Bhattacharyya, Pratip, 2005. "Of overlapping Cantor sets and earthquakes: analysis of the discrete Chakrabarti–Stinchcombe model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 199-215.
    25. Tamas Vicsek, 2001. "A question of scale," Nature, Nature, vol. 411(6836), pages 421-421, May.
    26. Gvozdanovic, Igor & Podobnik, Boris & Wang, Duan & Eugene Stanley, H., 2012. "1/f behavior in cross-correlations between absolute returns in a US market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(9), pages 2860-2866.
    27. Alexander M. Petersen & Fengzhong Wang & Shlomo Havlin & H. Eugene Stanley, 2010. "Market dynamics immediately before and after financial shocks: quantifying the Omori, productivity and Bath laws," Papers 1006.1882, arXiv.org, revised Oct 2010.
    28. D. Sornette, 2008. "Interdisciplinarity in Socio-economics, mathematical analysis and predictability of complex systems," Papers 0807.3814, arXiv.org.
    29. Telesca, Luciano, 2010. "Nonextensive analysis of seismic sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1911-1914.
    30. Minadakis, George & Potirakis, Stylianos M. & Nomicos, Constantinos & Eftaxias, Konstantinos, 2012. "Linking electromagnetic precursors with earthquake dynamics: An approach based on nonextensive fragment and self-affine asperity models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(6), pages 2232-2244.
    31. Chakrabarti, Bikas K & Stinchcombe, Robin B, 1999. "Stick-slip statistics for two fractal surfaces: a model for earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 270(1), pages 27-34.
    32. Siokis, Fotios M., 2012. "Stock market dynamics: Before and after stock market crashes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1315-1322.
    33. Minadakis, G. & Potirakis, S.M. & Stonham, J. & Nomicos, C. & Eftaxias, K., 2012. "The role of propagating stress waves on a geophysical scale: Evidence in terms of nonextensivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5648-5657.
    34. Kalimeri, M. & Papadimitriou, C. & Balasis, G. & Eftaxias, K., 2008. "Dynamical complexity detection in pre-seismic emissions using nonadditive Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1161-1172.
    35. Yan, Wanfeng & Woodard, Ryan & Sornette, Didier, 2012. "Diagnosis and prediction of rebounds in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1361-1380.
    36. S. M.D. Queirós & L. G. Moyano & J. de Souza & C. Tsallis, 2007. "A nonextensive approach to the dynamics of financial observables," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 161-167, January.
    37. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    38. Stanley, H.Eugene, 2000. "Exotic statistical physics: Applications to biology, medicine, and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 1-17.
    39. Silvio M. Duarte Queiros & Constantino Tsallis, 2005. "On the connection between financial processes with stochastic volatility and nonextensive statistical mechanics," Papers cond-mat/0502151, arXiv.org.
    40. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
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