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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

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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  • Silvio M. Duarte Queiros & Evaldo M. F. Curado & Fernando D. Nobre, 2011. "Minding impacting events in a model of stochastic variance," Papers 1102.4819, arXiv.org, revised Feb 2011.
    • Handle: RePEc:arx:papers:1102.4819
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    References listed on IDEAS

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    4. Sungmin Lee & Verónica C Ramenzoni & Petter Holme, 2010. "Emergence of Collective Memories," PLOS ONE, Public Library of Science, vol. 5(9), pages 1-7, September.
    5. Barunik, Jozef & Kristoufek, Ladislav, 2010. "On Hurst exponent estimation under heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3844-3855.
    6. Silvio M. Duarte Queiros, 2007. "On a generalised model for time-dependent variance with long-term memory," Papers 0705.3248, arXiv.org.
    7. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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