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Scaling theory of temporal correlations and size dependent fluctuations in the traded value of stocks

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  • Zoltan Eisler
  • Janos Kertesz

Abstract

Records of the traded value f_i(t) of stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average : sigma(i) ~ f(i)^alpha, with a strong time scale dependence alpha(dt). The non-trivial (i.e., neither 0.5 nor 1) value of alpha may have different origins and provides information about the microscopic dynamics. We present a set of recently discovered stylized facts, and then show their connection to such behavior. The functional form alpha(dt) originates from two aspects of the dynamics: Stocks of larger companies both tend to be traded in larger packages, and also display stronger correlations of traded value.

Suggested Citation

  • Zoltan Eisler & Janos Kertesz, 2005. "Scaling theory of temporal correlations and size dependent fluctuations in the traded value of stocks," Papers physics/0510058, arXiv.org, revised May 2006.
    • Handle: RePEc:arx:papers:physics/0510058
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    Cited by:

    1. Dror Y. Kenett & Xuqing Huang & Irena Vodenska & Shlomo Havlin & H. Eugene Stanley, 2014. "Partial correlation analysis: Applications for financial markets," Papers 1402.1405, arXiv.org.
    2. Chołoniewski, Jan & Chmiel, Anna & Sienkiewicz, Julian & Hołyst, Janusz A. & Küster, Dennis & Kappas, Arvid, 2016. "Temporal Taylor’s scaling of facial electromyography and electrodermal activity in the course of emotional stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 91-100.
    3. Aki-Hiro Sato & Takaki Hayashi & Janusz Hołyst, 2012. "Comprehensive analysis of market conditions in the foreign exchange market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(2), pages 167-179, October.
    4. Aki-Hiro Sato & Takaki Hayashi & Janusz A. Ho{l}yst, 2012. "Comprehensive Analysis of Market Conditions in the Foreign Exchange Market: Fluctuation Scaling and Variance-Covariance Matrix," Papers 1204.0426, arXiv.org.
    5. Gen Sakoda & Hideki Takayasu & Misako Takayasu, 2019. "Tracking Poisson Parameter for Non-Stationary Discontinuous Time Series with Taylor’s Abnormal Fluctuation Scaling," Stats, MDPI, vol. 2(1), pages 1-15, January.
    6. Xie, Rongrong & Deng, Shengfeng & Deng, Weibing & Pato, Mauricio P., 2022. "Generalized Poisson ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    7. Zoltan Eisler & Janos Kertesz, 2005. "Size matters: some stylized facts of the stock market revisited," Papers physics/0508156, arXiv.org, revised May 2006.
    8. Rudy Calif & François G. Schmitt, 2015. "Taylor Law in Wind Energy Data," Resources, MDPI, vol. 4(4), pages 1-9, October.
    9. Michelle B Graczyk & Sílvio M Duarte Queirós, 2017. "Intraday seasonalities and nonstationarity of trading volume in financial markets: Collective features," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-23, July.
    10. Dror Y. Kenett & Xuqing Huang & Irena Vodenska & Shlomo Havlin & H. Eugene Stanley, 2015. "Partial correlation analysis: applications for financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 15(4), pages 569-578, April.
    11. Qing Cai & Hai-Chuan Xu & Wei-Xing Zhou, 2016. "Taylor's Law of temporal fluctuation scaling in stock illiquidity," Papers 1610.01149, arXiv.org.

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