HAL : hal-00507759, version 1

arXiv : 1008.0054

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Detecting multiple change-points in general causal time series using penalized quasi-likelihood

Jean-Marc Bardet 1, William Chakry Kengne 1, Olivier Wintenberger 2

(30/07/2010)

This paper is devoted to the off-line multiple change-point detection in a semiparametric framework. The time series is supposed to belong to a large class of models including AR($\infty$), ARCH($\infty$), TARCH($\infty$),... models where the coefficients change at each instant of breaks. The different unknown parameters (number of changes, change dates and parameters of successive models) are estimated using a penalized contrast built on conditional quasi-likelihood. Under Lipshitzian conditions on the model, the consistency of the estimator is proved when the moment order $r$ of the process satisfies $r\geq 2$. If $r\geq 4$, the same convergence rates for the estimators than in the case of independent random variables are obtained. The particular cases of AR($\infty$), ARCH($\infty$) and TARCH($\infty$) show that our method notably improves the existing results.

1 :	Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM)
	Université Paris I - Panthéon Sorbonne
2 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine

Équipe de recherche : samm, ceremade

Domaine

:

Mathématiques/Statistiques Statistiques/Théorie

Mots Clés : Change detection – Causal processes – ARCH($\infty$) processes – AR($\infty$) processes – Quasi-maximum likelihood estimator – Model selection by penalized likelihood

hal-00507759, version 1

http://hal.archives-ouvertes.fr/hal-00507759

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Contributeur : Jean-Marc Bardet <>

Soumis le : Vendredi 30 Juillet 2010, 21:33:10

Dernière modification le : Samedi 31 Juillet 2010, 08:23:18