Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process

TL;DR

This paper develops a method to detect and estimate multiple abrupt change points in the long-range dependence or self-similarity parameter of a Gaussian process, providing theoretical guarantees and statistical tests.

Contribution

It introduces an estimator for multiple change points in Gaussian processes and proves its convergence properties along with a goodness-of-fit test for each segment.

Findings

Estimator satisfies a limit theorem with explicit convergence rate.

Central limit theorem established for parameter estimates within each segment.

A goodness-of-fit test is developed for the estimated segments.

Abstract

In this paper, an estimator of $m$ instants ($m$ is known) of abrupt changes of the parameter of long-range dependence or self-similarity is proved to satisfy a limit theorem with an explicit convergence rate for a sample of a Gaussian process. In each estimated zone where the parameter is supposed not to change, a central limit theorem is established for the parameter's (of long-range dependence, self-similarity) estimator and a goodness-of-fit test is also built. {\it To cite this article: J.M. Bardet, I. Kammoun, C. R. Acad. Sci. Paris, Ser. I 340 (2007).}