Analysis of many short time sequences: Forecast improvements achieved by shrinkage

Abstract

AbstractCredibility 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 we model the claim size yu in group i and at time t as the sum of three independent components: yit = μr + δi + ϵit. The first component, μt = μt−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 we show how to obtain forecasts from this model and we discuss the nature of the forecasts, with particular emphasis on shrinkage. We also assess the forecast improvements that can be expected from such a model. Finally, we discuss an extension of the above model which also allows the group offsets to change over time. We assume that the offsets for different groups follow independent random walks.