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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

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.

Suggested Citation

  • Vygintas Gontis & Aleksejus Kononovicius & Stefan Reimann, 2012. "The class of nonlinear stochastic models as a background for the bursty behavior in financial markets," Papers 1201.3083, arXiv.org, revised May 2012.
  • Handle: RePEc:arx:papers:1201.3083
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    File URL: http://arxiv.org/pdf/1201.3083
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    References listed on IDEAS

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    1. 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 1209-1227, July.
    2. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
    3. 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.
    4. 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.
    5. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
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    Cited by:

    1. Kononovicius, A. & Ruseckas, J., 2015. "Nonlinear GARCH model and 1/f noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 74-81.
    2. repec:eee:phsmap:v:483:y:2017:i:c:p:266-272 is not listed on IDEAS

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