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Power law distribution in high frequency financial data? An econometric analysis

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  • Todorova, Lora
  • Vogt, Bodo

Abstract

Power law distributions are very common in natural sciences. We analyze high frequency financial data from XETRA and the NYSE using maximum likelihood estimation and the Kolmogorov–Smirnov statistic to test whether the power law hypothesis holds also for these data. We find that the universality and scale invariance properties of the power law are violated. Furthermore, the returns of Daimler Chrysler and SAP traded simultaneously on both exchanges follow a power law at one exchange, but not at the other. These results raise some questions about the no-arbitrage condition. Finally, we find that an exponential function provides a better fit for the tails of the sample distributions than a power law function.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:23:p:4433-4444
    DOI: 10.1016/j.physa.2011.07.035
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    References listed on IDEAS

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    Cited by:

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    2. Johan Fellman, 2021. "Aspects of Pareto distributions," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 10(1), pages 1-4.
    3. Tao, Chen & Zhong, Guang-Yan & Li, Jiang-Cheng, 2023. "Dynamic correlation and risk resonance among industries of Chinese stock market: New evidence from time–frequency domain and complex network perspectives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    4. Janusz Mi'skiewicz, 2012. "Network analysis of correlation strength between the most developed countries," Papers 1211.3599, arXiv.org.

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