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Scale-free avalanche dynamics in the stock market

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  • Bartolozzi, M.
  • Leinweber, D.B.
  • Thomas, A.W.

Abstract

Self-organized criticality (SOC) has been claimed to play an important role in many natural and social systems. In the present work we empirically investigate the relevance of this theory to stock-market dynamics. Avalanches in stock-market indices are identified using a multi-scale wavelet-filtering analysis designed to remove Gaussian noise from the index. Here, new methods are developed to identify the optimal filtering parameters which maximize the noise removal. The filtered time series is reconstructed and compared with the original time series. A statistical analysis of both high-frequency Nasdaq E-mini Futures and daily Dow Jones data is performed. The results of this new analysis confirm earlier results revealing a robust power-law behaviour in the probability distribution function of the sizes, duration and laminar times between avalanches. This power-law behaviour holds the potential to be established as a stylized fact of stock market indices in general. While the memory process, implied by the power-law distribution of the laminar times, is not consistent with classical models for SOC, we note that a power-law distribution of the laminar times cannot be used to rule out self-organized critical behaviour.

Suggested Citation

  • Bartolozzi, M. & Leinweber, D.B. & Thomas, A.W., 2006. "Scale-free avalanche dynamics in the stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 132-139.
    • Handle: RePEc:eee:phsmap:v:370:y:2006:i:1:p:132-139
    DOI: 10.1016/j.physa.2006.04.024
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
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    1. Dupoyet, B. & Fiebig, H.R. & Musgrove, D.P., 2010. "Gauge invariant lattice quantum field theory: Implications for statistical properties of high frequency financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(1), pages 107-116.
    2. Zitis, Pavlos I. & Contoyiannis, Yiannis & Potirakis, Stelios M., 2022. "Critical dynamics related to a recent Bitcoin crash," International Review of Financial Analysis, Elsevier, vol. 84(C).
    3. M. Bartolozzi & C. Mellen, 2009. "Local Risk Decomposition for High-frequency Trading Systems," Papers 0904.4099, arXiv.org, revised Feb 2011.
    4. Ortega, Diego & Rodríguez-Laguna, Javier & Korutcheva, Elka, 2021. "Avalanches in an extended Schelling model: An explanation of urban gentrification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

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