  State-space models are widely used in many applications. In the domain of
count data, one such example is the model proposed by Harvey and Fernandes
(1989). Unlike many of its parameter-driven alternatives, this model is
observation-driven, leading to closed-form expressions for the predictive
density. In this paper, we demonstrate the need to extend the model of Harvey
and Fernandes (1989) by showing that their model is not variance stationary.
Our extension can accommodate for a wide range of variance processes that are
either increasing, decreasing, or stationary, while keeping the tractability of
the original model. Simulation and numerical studies are included to illustrate
the performance of our method.
