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Scaling and memory in the non-poisson process of limit order cancelation

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Author Info

  • Xiao-Hui Ni

    (ECUST)

  • Zhi-Qiang Jiang

    (ECUST)

  • Gao-Feng Gu

    (ECUST)

  • Fei Ren

    (ECUST)

  • Wei Chen

    (SZSE)

  • Wei-Xing Zhou

    (ECUST)

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    Abstract

    The order submission and cancelation processes are two crucial aspects in the price formation of stocks traded in order-driven markets. We investigate the dynamics of order cancelation by studying the statistical properties of inter-cancelation durations defined as the waiting times between consecutive order cancelations of 22 liquid stocks traded on the Shenzhen Stock Exchange of China in year 2003. Three types of cancelations are considered including cancelation of any limit orders, of buy limit orders and of sell limit orders. We find that the distributions of the inter-cancelation durations of individual stocks can be well modeled by Weibulls for each type of cancelation and the distributions of rescaled durations of each type of cancelations exhibit a scaling behavior for different stocks. Complex intraday patterns are also unveiled in the inter-cancelation durations. The detrended fluctuation analysis (DFA) and the multifractal DFA show that the inter-cancelation durations possess long-term memory and multifractal nature, which are not influenced by the intraday patterns. No clear crossover phenomenon is observed in the detrended fluctuation functions with respect to the time scale. These findings indicate that the cancelation of limit orders is a non-Poisson process, which has potential worth in the construction of order-driven market models.

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    File URL: http://arxiv.org/pdf/0911.0057
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0911.0057.

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    Date of creation: Oct 2009
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    Publication status: Published in Physica A 389 (2010) 2751-2761
    Handle: RePEc:arx:papers:0911.0057

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    Web page: http://arxiv.org/

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    1. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
    2. Francesco Mainardi & Marco Raberto & Rudolf Gorenflo & Enrico Scalas, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Papers cond-mat/0006454, arXiv.org, revised Nov 2000.
    3. Szabolcs Mike & J. Doyne Farmer, 2007. "An empirical behavioral model of liquidity and volatility," Papers 0709.0159, arXiv.org.
    4. Sergei Maslov & Mark Mills, 2001. "Price fluctuations from the order book perspective - empirical facts and a simple model," Papers cond-mat/0102518, arXiv.org.
    5. Fei Ren & Gao-Feng Gu & Wei-Xing Zhou, 2009. "Scaling and memory in the return intervals of realized volatility," Papers 0904.1107, arXiv.org, revised Aug 2009.
    6. Lillo Fabrizio & Farmer J. Doyne, 2004. "The Long Memory of the Efficient Market," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-35, September.
    7. S. M.D. Queirós & L. G. Moyano & J. de Souza & C. Tsallis, 2007. "A nonextensive approach to the dynamics of financial observables," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(2), pages 161-167, 01.
    8. Zhiguang (Gerald) Wang, 2009. "Volatility Risk," Issue Briefs 2009513, South Dakota State University, Department of Economics.
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