Practical conditions for the convergence of the maximum likelihood estimator in observation-driven models

Randal Douc (1) , François Roueff (2) , Tepmony Sim (2)

1 TSP - CITI - Communications, Images et Traitement de l'Information
2 LTCI - Laboratoire Traitement et Communication de l'Information

This paper generalizes asymptotic properties obtained in the observation-driven times series models considered by \cite{dou:kou:mou:2013} in the sense that the conditional law of each observation is also permitted to depend on the parameter. The existence of ergodic solutions and the consistency of the Maximum Likelihood Estimator (MLE) are derived under easy-to-check conditions. The obtained conditions, however, appear to apply for a wide class of models. We illustrate our results with two recently introduced observation-driven times series, namely, the NBIN-GARCH and the NM-GARCH, demonstrating the consistency of the MLE for these two models.

Mots clés: maximum likelihood; consistency; ergodicity; observation-driven models; time series of counts

Domaines: Statistiques [stat]

Randal Douc, François Roueff, Tepmony Sim. Practical conditions for the convergence of the maximum likelihood estimator in observation-driven models. 2014. ⟨hal-01078073v1⟩