An observation-driven state-space count model for experience rating

State-space models are widely used in applications, e.g., in economics, finance and actuarial science. 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, and it leads to a closed-form expression for the predictive density. This predictive density takes into account past observations by assigning a seniority weighting to them. This feature makes this model very appealing for general insurance ratemaking. However, the model of Harvey and Fernandes (1989) has the property that the variance diverges in the long-run, which might be an undesirable model feature. In this paper, we extend the model of Harvey and Fernandes (1989) by allowing for flexible variance specifications including non-explosive ones, while keeping the model fully tractable.