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Nonextensive statistical features of the Polish stock market fluctuations

Author

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  • Rak, R.
  • Drożdż, S.
  • Kwapień, J.

Abstract

The statistics of return distributions on various time scales constitutes one of the most informative characteristics of the financial dynamics. Here, we present a systematic study of such characteristics for the Polish stock market index WIG20 over the period 04.01.1999–31.10.2005 for the time lags ranging from 1min up to 1h. This market is commonly classified as emerging. Still on the shortest time scales studied we find that the tails of the return distributions are consistent with the inverse cubic power law, as identified previously for majority of the mature markets. Within the time scales studied, a quick and considerable departure from this law towards a Gaussian can however be traced. Interestingly, all the forms of the distributions observed can be comprised by the single q-Gaussians which provide a satisfactory and at the same time compact representation of the distribution of return fluctuations over all magnitudes of their variation. The corresponding nonextensivity parameter q was found to systematically decrease when increasing the time scales. The temporal correlations quantified here in terms of multifractality provide further arguments in favor of nonextensivity.

Suggested Citation

  • Rak, R. & Drożdż, S. & Kwapień, J., 2007. "Nonextensive statistical features of the Polish stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 315-324.
    • Handle: RePEc:eee:phsmap:v:374:y:2007:i:1:p:315-324
    DOI: 10.1016/j.physa.2006.07.035
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    Cited by:

    1. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Federica De Domenico & Giacomo Livan & Guido Montagna & Oreste Nicrosini, 2023. "Modeling and Simulation of Financial Returns under Non-Gaussian Distributions," Papers 2302.02769, arXiv.org.
    3. Łukasz Bil & Dariusz Grech & Magdalena Zienowicz, 2017. "Asymmetry of price returns—Analysis and perspectives from a non-extensive statistical physics point of view," PLOS ONE, Public Library of Science, vol. 12(11), pages 1-24, November.
    4. Pan, Raj Kumar & Sinha, Sitabhra, 2008. "Inverse-cubic law of index fluctuation distribution in Indian markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2055-2065.
    5. Todorova, Lora & Vogt, Bodo, 2011. "Power law distribution in high frequency financial data? An econometric analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4433-4444.
    6. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2021. "Financial Return Distributions: Past, Present, and COVID-19," Papers 2107.06659, arXiv.org.
    7. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    8. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    9. Trindade, Marco A.S. & Floquet, Sergio & Filho, Lourival M. Silva, 2020. "Portfolio theory, information theory and Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    10. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.
    11. Kostanjcar, Zvonko & Jeren, Branko & Juretic, Zeljan, 2012. "Impact of uncertainty in expected return estimation on stock price volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5563-5571.
    12. Second Bwanakare, 2023. "Energy Efficiency Forecast as an Inverse Stochastic Problem: A Cross-Entropy Econometrics Approach," Energies, MDPI, vol. 16(23), pages 1-16, November.

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