A test for parameter change in general causal time series using quasi-likelihood estimator

Charky Kengne, William

doi:10.1016/j.crma.2012.03.001

Statistics

A test for parameter change in general causal time series using quasi-likelihood estimator
[Utilisation de la quasi-vraisemblance pour un test de détection de rupture dans les paramètres des processus causaux]

Présenté par : the Editorial Board

Charky Kengne, William ^1,²

¹ SAMM, Université Paris 1 Panthéon-Sorbonne, 90 rue de Tolbiac, 75013 Paris, France
² ENSP, Université de Yaoundé I, BP 8390, Yaoundé, Cameroon

Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 307-312.

Résumé
Abstract

Dans cette Note, nous proposons un nouveau test de détection de rupture dans le paramètre dʼun processus $X = {(X_{t})}_{t \in Z}$ appartenant à une classe de processus causaux contenant les modèles AR(∞), ARCH(∞), TARCH(∞), … . Deux statistiques ${\hat{Q}}_{n}^{(1)}$ et ${\hat{Q}}_{n}^{(2)}$ sont construites en utilisant lʼestimateur du maximum de quasi-vraisemblance du paramètre. Sous lʼhypothèse nulle selon laquelle aucun changement nʼintervient dans le paramètre, chacune de ces statistiques converge vers une distribution connue et le maximum diverge vers lʼinfini sous lʼhypothèse alternative dʼune rupture. Quelques résultats de simulations sont présentés.

In this Note, we propose a new procedure to test a change in the parameter of a process $X = {(X_{t})}_{t \in Z}$ belonging to a class of causal models including AR(∞), ARCH(∞), TARCH(∞), … models. Two statistics ${\hat{Q}}_{n}^{(1)}$ and ${\hat{Q}}_{n}^{(2)}$ are constructed using the quasi-likelihood estimator (QMLE) of the parameter. Under the null hypothesis that there is no change, each of these statistics converges weakly to a well-known distribution and the maximum diverges to infinity under the alternative of one change. Some simulation results are reported.

Reçu le : 2011-07-11
Accepté le : 2012-03-01
Publié le : 2012-03-01

DOI : 10.1016/j.crma.2012.03.001

Affiliations des auteurs :

Charky Kengne, William ^{1, 2}

¹ SAMM, Université Paris 1 Panthéon-Sorbonne, 90 rue de Tolbiac, 75013 Paris, France
² ENSP, Université de Yaoundé I, BP 8390, Yaoundé, Cameroon

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     title = {A test for parameter change in general causal time series using quasi-likelihood estimator},
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Charky Kengne, William. A test for parameter change in general causal time series using quasi-likelihood estimator. Comptes Rendus. Mathématique, Tome 350 (2012) no. 5-6, pp. 307-312. doi : 10.1016/j.crma.2012.03.001. http://www.numdam.org/articles/10.1016/j.crma.2012.03.001/

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