Detecting changes in the fluctuations of a Gaussian process and an application to heartbeat time series
| dc.creator | Bardet, Jean-Marc | |
| dc.creator | Kammoun, Imen | |
| dc.date | 2007-12-07 | |
| dc.date.accessioned | 2026-07-07T08:47:57Z | |
| dc.date.available | 2026-07-07T08:47:57Z | |
| dc.description | The aim of this paper is first the detection of multiple abrupt changes of the long-range dependence (respectively self-similarity, local fractality) parameters from a sample of a Gaussian stationary times series (respectively time series, continuous-time process having stationary increments). The estimator of the $m$ change instants (the number $m$ is supposed to be known) is proved to satisfied a limit theorem with an explicit convergence rate. Moreover, a central limit theorem is established for an estimator of each long-range dependence (respectively self-similarity, local fractality) parameter. Finally, a goodness-of-fit test is also built in each time domain without change and proved to asymptotically follow a Khi-square distribution. Such statistics are applied to heart rate data of marathon's runners and lead to interesting conclusions. | |
| dc.identifier | https://arxiv.org/abs/0712.1157 | |
| dc.identifier | http://arxiv.org/abs/0712.1157 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/143779 | |
| dc.subject | Statistics Theory | |
| dc.title | Detecting changes in the fluctuations of a Gaussian process and an application to heartbeat time series | |
| dc.type | text |