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Segmentation algorithm for non-stationary compound Poisson processes

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  • Bence Toth
  • Fabrizio Lillo
  • J. Doyne 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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File URL: http://arxiv.org/pdf/1001.2549
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1001.2549.

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Date of creation: Jan 2010
Date of revision: Feb 2011
Publication status: Published in Eur. Phys. J. B 78, 235-243 (2010)
Handle: RePEc:arx:papers:1001.2549

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Web page: http://arxiv.org/

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  1. Austin Gerig, 2008. "A Theory for Market Impact: How Order Flow Affects Stock Price," Papers 0804.3818, arXiv.org, revised Jul 2008.
  2. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
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Cited by:
  1. 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, vol. 6(5), pages 1-81.
  2. 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.
  3. Bence Toth & Zoltan Eisler & Fabrizio Lillo & Julien Kockelkoren & Jean-Philippe Bouchaud & J. Doyne Farmer, 2011. "How does the market react to your order flow?," Papers 1104.0587, arXiv.org, revised May 2012.
  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. 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.

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