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

TL;DR

This paper develops statistical methods to detect multiple change points in Gaussian processes, including applications to heartbeat time series, providing estimators with proven convergence and distribution properties.

Contribution

It introduces new estimators for change points and parameters in Gaussian processes, with proven limit theorems and a goodness-of-fit test, applied to real heartbeat data.

Findings

Effective detection of change points in heart rate data.

Estimators satisfy limit theorems with explicit convergence rates.

Goodness-of-fit test follows a Chi-square distribution asymptotically.

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 $m$ 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.