Minding impacting events in a model of stochastic variance
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1102.4819.
Date of creation: Feb 2011
Date of revision: Feb 2011
Publication status: Published in PLoS ONE 6(3): e18149 (2011)
Contact details of provider:
Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stefan Thurner & J. Doyne Farmer & John Geanakoplos, 2009.
"Leverage Causes Fat Tails and Clustered Volatility,"
0908.1555, arXiv.org, revised Jan 2010.
- Stefan Thurner & J. Doyne Farmer & John Geanakoplos, 2012. "Leverage causes fat tails and clustered volatility," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 695-707, February.
- Stefan Thurner & J. Doyne Farmer & John Geanakoplos, 2010. "Leverage Causes Fat Tails and Clustered Volatility," Cowles Foundation Discussion Papers 1745, Cowles Foundation for Research in Economics, Yale University.
- Stefan Thurner & J. Doyne Farmer & John Geanakoplos, 2010. "Leverage Causes Fat Tails and Clustered Volatility," Cowles Foundation Discussion Papers 1745R, Cowles Foundation for Research in Economics, Yale University, revised Nov 2011.
- Jozef Barunik & Ladislav Kristoufek, 2012.
"On Hurst exponent estimation under heavy-tailed distributions,"
- 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.
- Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators).
If references are entirely missing, you can add them using this form.