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

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

1 SAMOS - Statistique Appliquée et MOdélisation Stochastique
2 CES - Centre d'économie de la Sorbonne

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).}

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

Jean-Marc Bardet, Imen Kammoun. Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process. 2007. ⟨hal-00195089v2⟩