Statistics
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.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.05.007
Bardet, Jean-Marc 1; Kammoun, Imen 1

1 Université Paris 1, SAMOS-MATISSE-CES, 90, rue de Tolbiac, 75013 Paris, France
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Bardet, Jean-Marc; Kammoun, Imen. 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. http://www.numdam.org/articles/10.1016/j.crma.2008.05.007/

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