Ergodicity of observation-driven time series models and consistency of   the maximum likelihood estimator
  This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The consistency of the maximum likelihood estimators is then derived for well- specified and misspecified models. 
Randal Douc, Paul Doukhan and Eric Moulines
math.ST stat.TH