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The non-random walk of stock prices: The long-term correlation between signs and sizes

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  • Gabriele La Spada
  • J. Doyne Farmer
  • Fabrizio Lillo

Abstract

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.

Suggested Citation

  • Gabriele La Spada & J. Doyne Farmer & Fabrizio Lillo, 2007. "The non-random walk of stock prices: The long-term correlation between signs and sizes," Papers 0711.4596, arXiv.org, revised May 2008.
    • Handle: RePEc:arx:papers:0711.4596
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    Cited by:

    1. Lisana B. Martinez & M. Belén Guercio & Aurelio Fernandez Bariviera & Antonio Terceño, 2018. "The impact of the financial crisis on the long-range memory of European corporate bond and stock markets," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 45(1), pages 1-15, February.
    2. Z. Sun & P. A. Hamill & Y. Li & Y. C. Yang & S. A. Vigne, 2019. "Did long-memory of liquidity signal the European sovereign debt crisis?," Annals of Operations Research, Springer, vol. 282(1), pages 355-377, November.
    3. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-16, July.
    4. Bariviera, Aurelio F. & Basgall, María José & Hasperué, Waldo & Naiouf, Marcelo, 2017. "Some stylized facts of the Bitcoin market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 82-90.
    5. Kirchler, Michael & Huber, Jürgen, 2009. "An exploration of commonly observed stylized facts with data from experimental asset markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1631-1658.
    6. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2010. "Complex stock trading network among investors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4929-4941.
    7. Assaf Almog & Ferry Besamusca & Mel MacMahon & Diego Garlaschelli, 2015. "Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations," Papers 1504.00590, arXiv.org.
    8. Ji, Aiwen & Shang, Pengjian, 2019. "Analysis of financial time series through forbidden patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).

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