On a generalised model for time-dependent variance with long-term memory
| dc.creator | Queiros, Silvio M. Duarte | |
| dc.date | 2007-05-23 | |
| dc.date.accessioned | 2026-07-07T12:05:14Z | |
| dc.date.available | 2026-07-07T12:05:14Z | |
| dc.description | The 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.description | 6 pages, 4 figures | |
| dc.identifier | https://arxiv.org/abs/0705.3248 | |
| dc.identifier | http://arxiv.org/abs/0705.3248 | |
| dc.identifier | EPL, 80 (2007) 30005 | |
| dc.identifier | doi:10.1209/0295-5075/80/30005 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/208323 | |
| dc.subject | Data Analysis, Statistics and Probability | |
| dc.subject | Statistical Finance | |
| dc.title | On a generalised model for time-dependent variance with long-term memory | |
| dc.type | text |