Detecting changes in the fluctuations of a Gaussian process and an application to heartbeat time series
Abstract
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 change instants (the number 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.
Keywords
Cite
@article{arxiv.0712.1157,
title = {Detecting changes in the fluctuations of a Gaussian process and an application to heartbeat time series},
author = {Jean-Marc Bardet and Imen Kammoun},
journal= {arXiv preprint arXiv:0712.1157},
year = {2007}
}