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.

翻译：状态空间模型广泛应用于众多领域。在计数数据领域，一个典型例子是Harvey与Fernandes（1989）提出的模型。与许多参数驱动替代模型不同，该模型属于观测驱动模型，可得到预测密度的闭合表达式。本文通过证明Harvey-Fernandes模型并非方差平稳，论证了扩展该模型的必要性。我们提出的扩展模型能够容纳广泛方差过程（包括递增、递减或平稳方差过程），同时保持原模型的可处理性。文中包含模拟与数值研究以阐明所提方法的性能。