Sequential change-point detection in Poisson autoregressive models

Kengne, William

Journal de la société française de statistique, Tome 156 (2015) no. 4, pp. 98-112.

Nous considérons la détection séquentielle de ruptures dans une classe assez générale de modèles de Poisson autorégressifs de séries temporelles à valeurs entières. La moyenne conditionnelle du processus dépend d’un paramètre ${\theta }_0^{*}\in \Theta \subset I{R}^d$ susceptible de changer dans le temps au fur et à mesure que les données sont observées. Nous proposons une procédure séquentielle dont le temps de suivi peut être fini ou infini basée sur l’estimateur du maximum de vraisemblance du paramètre. Sous l’hypothèse nulle selon laquelle aucun changement n’intervient dans le paramètre, la statistique de test converge vers une distribution connue. Des résultats de simulations nous permettent d’évaluer la puissance (empirique) ainsi que l’efficacité en terme du délai de détection et un exemple d’application aux données réelles est fourni.

We consider the sequential change-point detection in a general class of Poisson autoregressive models. The conditional mean of the process depends on a parameter${\theta }_0^{*}\in \Theta \subset I{R}^d$ which may change over time as and when data are observed. We propose a closed and open-end procedure based on the maximum likelihood estimator of the parameter. Under the null hypothesis of no change, it is shown that the detector converges to a well know distribution. The (empirical) power and the efficiency in terms of the detection delay are assessed through a simulation study and a real data example is provided.

Keywords: Sequential detection, change-point, time series of counts, Poisson autoregression, likelihood estimation
Mot clés : Détection séquentielle, rupture, séries temporelles à valeurs entières, autorégression de Poisson, estimation par vraisemblance

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