Some recent theory for autoregressive count time series

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Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator (2012, methodology): “Among the models proposed so far, observation-driven models introduced by Cox (1981) plays an important role (see (Kedem and Fokianos, 2002, Chapter 4) for a comprehensive account and Tjøstheim (2012) for a recent survey).”
Poisson QMLE of Count Time Series Models (2016, methodology): “E-mail: christian.francq@univ-lille3.fr 1Even if the probabilistic structure, in particular the ergodicity, of these models is not easy to derive (Tjøstheim (2012, 2015) and the references therein).”