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Segmentation algorithm for non-stationary compound Poisson processes

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  • B. Tóth

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  • F. Lillo
  • J. D. Farmer

Abstract

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated to a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galvan, et al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm outperforms the original one for regime switching compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one.
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Suggested Citation

  • B. Tóth & F. Lillo & J. D. Farmer, 2010. "Segmentation algorithm for non-stationary compound Poisson processes," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 78(2), pages 235-243, November.
  • Handle: RePEc:spr:eurphb:v:78:y:2010:i:2:p:235-243
    DOI: 10.1140/epjb/e2010-10046-8
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    References listed on IDEAS

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    1. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner (ed.), 2009. "Handbook of Financial Markets: Dynamics and Evolution," Elsevier Monographs, Elsevier, edition 1, number 9780123742582, August.
    2. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    3. Austin Gerig, 2008. "A Theory for Market Impact: How Order Flow Affects Stock Price," Papers 0804.3818, arXiv.org, revised Jul 2008.
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    1. repec:eee:phsmap:v:490:y:2018:i:c:p:439-450 is not listed on IDEAS
    2. B. Tóth & Z. Eisler & F. Lillo & J. Kockelkoren & J.-P. Bouchaud & J.D. Farmer, 2012. "How does the market react to your order flow?," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1015-1024, May.
    3. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2011. "The Japanese economy in crises: A time series segmentation study," Economics Discussion Papers 2011-24, Kiel Institute for the World Economy (IfW).
    4. Michele Tumminello & Fabrizio Lillo & Jyrki Piilo & Rosario N. Mantegna, 2011. "Identification of clusters of investors from their real trading activity in a financial market," Papers 1107.3942, arXiv.org.
    5. Kucharczyk, Daniel & Wyłomańska, Agnieszka & Zimroz, Radosław, 2017. "Structural break detection method based on the Adaptive Regression Splines technique," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 499-511.
    6. Bence Toth & Yves Lemperiere & Cyril Deremble & Joachim de Lataillade & Julien Kockelkoren & Jean-Philippe Bouchaud, 2011. "Anomalous price impact and the critical nature of liquidity in financial markets," Papers 1105.1694, arXiv.org, revised Nov 2011.
    7. Jonathan Donier & Julius Bonart, 2014. "A Million Metaorder Analysis of Market Impact on the Bitcoin," Papers 1412.4503, arXiv.org, revised Sep 2015.
    8. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2012. "The Japanese economy in crises: A time series segmentation study," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy (IfW), vol. 6, pages 1-81.
    9. Zhang, Yiting & Lee, Gladys Hui Ting & Wong, Jian Cheng & Kok, Jun Liang & Prusty, Manamohan & Cheong, Siew Ann, 2011. "Will the US economy recover in 2010? A minimal spanning tree study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2020-2050.

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