On a generalised model for time-dependent variance with long-term memory

dc.creatorQueiros, Silvio M. Duarte
dc.date2007-05-23
dc.date.accessioned2026-07-07T12:05:14Z
dc.date.available2026-07-07T12:05:14Z
dc.descriptionThe ARCH process (R. F. Engle, 1982) constitutes a paradigmatic generator of stochastic time series with time-dependent variance like it appears on a wide broad of systems besides economics in which ARCH was born. Although the ARCH process captures the so-called "volatility clustering" and the asymptotic power-law probability density distribution of the random variable, it is not capable to reproduce further statistical properties of many of these time series such as: the strong persistence of the instantaneous variance characterised by large values of the Hurst exponent (H > 0.8), and asymptotic power-law decay of the absolute values self-correlation function. By means of considering an effective return obtained from a correlation of past returns that has a q-exponential form we are able to fix the limitations of the original model. Moreover, this improvement can be obtained through the correct choice of a sole additional parameter, $q_{m}$. The assessment of its validity and usefulness is made by mimicking daily fluctuations of SP500 financial index.
dc.description6 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0705.3248
dc.identifierhttp://arxiv.org/abs/0705.3248
dc.identifierEPL, 80 (2007) 30005
dc.identifierdoi:10.1209/0295-5075/80/30005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208323
dc.subjectData Analysis, Statistics and Probability
dc.subjectStatistical Finance
dc.titleOn a generalised model for time-dependent variance with long-term memory
dc.typetext

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