This paper presents statistical models which lead to experience rating in insurance. Serial correlation for risk variables can receive endogeneous or exogeneous explanations. The interpretation retained by actuarial models is exogeneous and reflects the positive contagion usually observed for the number of claims. This positive contagion can be explained by the revelation throughout time of a hidden features in the risk distributions. These features are represented by fixed effects which are predicted with a random effects model. This article discusses identification issues on the nature of the dynamics of non-life insurance data. Example of predictions are given for count data models with a constant or time-varying random effects, one or several equations, and for cost-number models on events.
