Comptes Rendus
no. 13-14
Statistics
Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process
[Détection de ruptures du paramètre de longue mémoire, d'autosimilarité pour des processus gaussiens]

Présenté par : Paul Deheuvels

Jean-Marc Bardet1 ; Imen Kammoun1
1 Université Paris 1, SAMOS-MATISSE-CES, 90, rue de Tolbiac, 75013 Paris, France
Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 789-794.

Dans cette Note, pour une trajectoire d'un processus gaussien, un estimateur des m points de ruptures (m est supposé connu) du paramètre de longue mémoire ou d'autosimilarité est construit et on montre qu'il vérifie un théorème limite avec une vitesse de convergence explicite. Dans chaque zone (estimée) où ce paramètre est constant, un estimateur de ce paramètre vérifie un théorème limite centrale et un test d'ajustement est également mis en place.

In this Note, 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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.05.007
Jean-Marc Bardet 1 ; Imen Kammoun 1

1 Université Paris 1, SAMOS-MATISSE-CES, 90, rue de Tolbiac, 75013 Paris, France 
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Jean-Marc Bardet; Imen Kammoun. Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process. Comptes Rendus. Mathématique, Volume 346 (2008) no. 13-14, pp. 789-794. doi : 10.1016/j.crma.2008.05.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.007/

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