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The class of nonlinear stochastic models as a background for the bursty behavior in financial markets

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  • Vygintas Gontis
  • Aleksejus Kononovicius
  • Stefan Reimann
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    Abstract

    We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process with known first hitting (first passage) time statistics. Using these results we derive PDF of burst duration for the proposed model. We confirm analytical expressions by numerical evaluation and discuss bursty behavior of return in financial markets in the framework of modeling by nonlinear SDE.

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    File URL: http://arxiv.org/pdf/1201.3083
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1201.3083.

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    Date of creation: Jan 2012
    Date of revision: May 2012
    Publication status: Published in Advances in Complex Systems 15 (1), 2012, 1250071
    Handle: RePEc:arx:papers:1201.3083

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    1. Friedrich Wagner & Thomas Lux & Simone Alfarano, 2005. "Time-Variation of Higher Moments in a Financial Market with Heterogeneous Agents: An Analytical Approach," Working Papers wp05-02, Warwick Business School, Finance Group.
    2. Kononovicius, A. & Gontis, V., 2012. "Agent based reasoning for the non-linear stochastic models of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1309-1314.
    3. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
    4. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Society for Computational Economics, vol. 26(1), pages 19-49, August.
    5. Gontis, V. & Kaulakys, B., 2004. "Multiplicative point process as a model of trading activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 505-514.
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