Detecting changes in the fluctuations of a Gaussian process and an application to heartbeat time series

Jean-Marc Bardet (1, 2) , Imen Kammoun (1, 2)

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 MATISSE - UMR 8595 - Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques

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.

Mots clés: Long-range dependent processes; Self-similar processes; Detection of abrupt changes; Hurst parameter; Self-similarity parameter; Wavelet analysis; Goodness-of-fit test.; Goodness-of-fit test

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jean-Marc Bardet, Imen Kammoun. Detecting changes in the fluctuations of a Gaussian process and an application to heartbeat time series. 2007. ⟨hal-00194909⟩