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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.

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File URL: http://arxiv.org/pdf/0711.4596
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0711.4596.

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Date of creation: Nov 2007
Date of revision: May 2008
Handle: RePEc:arx:papers:0711.4596

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Web page: http://arxiv.org/

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Cited by:
  1. 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.
  2. Kirchler, Michael & Huber, J├╝rgen, 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.

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