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.
Accepted:
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Jean-Marc Bardet 1; Imen Kammoun 1
@article{CRMATH_2008__346_13-14_789_0, author = {Jean-Marc Bardet and Imen Kammoun}, title = {Detecting abrupt changes of the long-range dependence or the self-similarity of a {Gaussian} process}, journal = {Comptes Rendus. Math\'ematique}, pages = {789--794}, publisher = {Elsevier}, volume = {346}, number = {13-14}, year = {2008}, doi = {10.1016/j.crma.2008.05.007}, language = {en}, }
TY - JOUR AU - Jean-Marc Bardet AU - Imen Kammoun TI - Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process JO - Comptes Rendus. Mathématique PY - 2008 SP - 789 EP - 794 VL - 346 IS - 13-14 PB - Elsevier DO - 10.1016/j.crma.2008.05.007 LA - en ID - CRMATH_2008__346_13-14_789_0 ER -
%0 Journal Article %A Jean-Marc Bardet %A Imen Kammoun %T Detecting abrupt changes of the long-range dependence or the self-similarity of a Gaussian process %J Comptes Rendus. Mathématique %D 2008 %P 789-794 %V 346 %N 13-14 %I Elsevier %R 10.1016/j.crma.2008.05.007 %G en %F CRMATH_2008__346_13-14_789_0
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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