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Minding impacting events in a model of stochastic variance

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  • Silvio M. Duarte Queiros
  • Evaldo M. F. Curado
  • Fernando D. Nobre
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    Abstract

    We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold and another one when the local standard deviation outnumbers it. In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterised by large values of the Hurst exponent is greater than 0.8, which are ubiquitous features in complex systems.

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    File URL: http://arxiv.org/pdf/1102.4819
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1102.4819.

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    Date of creation: Feb 2011
    Date of revision: Feb 2011
    Publication status: Published in PLoS ONE 6(3): e18149 (2011)
    Handle: RePEc:arx:papers:1102.4819

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    1. Stefan Thurner & J. Doyne Farmer & John Geanakoplos, 2009. "Leverage Causes Fat Tails and Clustered Volatility," Papers 0908.1555, arXiv.org, revised Jan 2010.
    2. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, Elsevier, vol. 45(1-2), pages 7-38.
    3. Barunik, Jozef & Kristoufek, Ladislav, 2010. "On Hurst exponent estimation under heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 389(18), pages 3844-3855.
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