Estimating the parameters of a seasonal Markov-modulated Poisson process

Armelle Guillou (1) , Stéphane Loisel (2) , Gilles Stupfler (3)

1 IRMA - Institut de Recherche Mathématique Avancée
2 SAF - Laboratoire de Sciences Actuarielle et Financière
3 CERGAM - Centre d'Études et de Recherche en Gestion d'Aix-Marseille

Motivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a small simulation study and a real data analysis.

Mots clés: Markov-modulated Poisson process; Seasonality; Split-time likelihood; Strong consistency; Asymptotic normality

Domaines: Théorie [stat.TH]

Armelle Guillou, Stéphane Loisel, Gilles Stupfler. Estimating the parameters of a seasonal Markov-modulated Poisson process. Statistical Methodology, 2015, 26, pp.103-123. ⟨10.1016/j.stamet.2015.04.003⟩. ⟨hal-00965279v2⟩