We study count processes in insurance, in which the underlying risk factor is time varying and unobservable. The factor follows an autoregressive gamma process, and the resulting model generalizes the static Poisson‐Gamma model and allows for closed form expression for the posterior Bayes (linear or nonlinear) premium. Moreover, the estimation and forecasting can be conducted within the same framework in a rather efficient way. An example of automobile insurance pricing illustrates the ability of the model to capture the duration dependent, nonlinear impact of past claims on future ones and the improvement of the Bayes pricing method compared to the linear credibility approach.