Credibility models in actuarial science deal with multiple short time series where each series represents claim amounts of different insurance groups. Commonly used credibility models imply shrinkage of group-specific estimates towards their average. In this paper the authors model the claim size yit in group i and at time t as the sum of three independent components: yit=μt+δi+•it. The first component, μt=μtÅ-1+mt, represents time-varying levels that are common to all groups. The second component, δi, represents random group offsets that are the same in all periods, and the third component represents independent measurement errors. In this paper the authors show how to obtain forecasts from this model and they discuss the nature of the forecasts, with particular emphasis on shrinkage. The authors also assess the forecast improvements that can be expected from such a model. Finally, they discuss an extension of the above model which also allows the group offset to change over time. The authors assume that the offsets for different groups follow independent random walks.
