Stationarity of a general class of observation driven models for discrete valued processes

A large variety of time series observation-driven models for binary and count data are currently used in different contexts. Despite the importance of stationarity and ergodicity to ensure suitable results, for many of these models stationarity is not yet proved. We specify a general class of observation-driven models for discrete valued processes, which encompasses the most frequently used models. Then, we show strict stationarity by means of Feller properties and establish easy-to-check stationarity conditions.