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On the gap between an empirical distribution and an exponential distribution of waiting times for price changes in a financial market

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  • Sazuka, Naoya

Abstract

We analyze waiting times for price changes in a foreign currency exchange rate. Recent empirical studies of high-frequency financial data support that trades in financial markets do not follow a Poisson process and the waiting times between trades are not exponentially distributed. Here we show that our data is well approximated by a Weibull distribution rather than an exponential distribution in the non-asymptotic regime. Moreover, we quantitatively evaluate how much an empirical data is far from an exponential distribution using a Weibull fit. Finally, we discuss a transition between a Weibull-law and a power-law in the long time asymptotic regime.

Suggested Citation

  • Sazuka, Naoya, 2007. "On the gap between an empirical distribution and an exponential distribution of waiting times for price changes in a financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 500-506.
    • Handle: RePEc:eee:phsmap:v:376:y:2007:i:c:p:500-506
    DOI: 10.1016/j.physa.2006.10.094
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    Citations

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    Cited by:

    1. Takero Ibuki & Jun-ichi Inoue, 2011. "Response of double-auction markets to instantaneous Selling–Buying signals with stochastic Bid–Ask spread," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 6(2), pages 93-120, November.
    2. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2009. "Detrended fluctuation analysis of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 433-440.
    3. A. Saichev & D. Sornette, 2012. "A simple microstructure return model explaining microstructure noise and Epps effects," Papers 1202.3915, arXiv.org.
    4. Sazuka, Naoya & Inoue, Jun-ichi & Scalas, Enrico, 2009. "The distribution of first-passage times and durations in FOREX and future markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2839-2853.
    5. Ren, Fei & Guo, Liang & Zhou, Wei-Xing, 2009. "Statistical properties of volatility return intervals of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 881-890.
    6. Niu, Hongli & Wang, Weiqing & Zhang, Junhuan, 2019. "Recurrence duration statistics and time-dependent intrinsic correlation analysis of trading volumes: A study of Chinese stock indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 838-854.
    7. Jiang, Zhi-Qiang & Chen, Wei & Zhou, Wei-Xing, 2008. "Scaling in the distribution of intertrade durations of Chinese stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5818-5825.
    8. Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2025-2034.
    9. Niu, Hongli & Wang, Jun, 2017. "Return volatility duration analysis of NYMEX energy futures and spot," Energy, Elsevier, vol. 140(P1), pages 837-849.
    10. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
    11. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.

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