Time series models for the credibility estimation of insurance premiums

Simple time-series models for the analysis of cross-sectional time-series data are developed in this thesis. These models are particularly relevant for the analysis of actuarial data that arise in the insurance ratemaking problem. Traditional credibility models of insurance ratemaking assume that the model components are time-invariant and that the importance of past data does not depend on the age of the observations. The models that are proposed in this thesis incorporate the cross-sectional pooling aspect of credibility models, but they also allow for a time-varying nature of the model components.; A somewhat heuristic, but practically useful forecasting method is suggested. It allows for the components of traditional credibility model to change over time, yet still provides shrinkage at the forecast origin. The analysis of automobile insurance data illustrates the feasibility of this approach and the potential forecast improvement that can be expected from this method.; Model-based forecast approaches are also suggested. These models combine common time-varying trend and seasonal components with offsets that are allowed to change over time. The nature of the forecasts that are implied by these models is discussed. It is shown that estimates of the model components can be updated through easy recursive equations. Forecasts from the common time-varying level model, which represents a special case of suggested models, are determined by a combination of cross-sectional pooling and the exponential smoothing. Maximum likelihood estimation of the model parameters, as well as an alternative estimation procedure that simplifies the computation, are developed. A method for computing the mean squared error (MSE) of one-step-ahead forecasts that result from each of suggested forecast methods is discussed. This information is then used to assess the performance of the forecasting methods. The practical usefulness of the suggested model-based approaches is illustrated through the analysis of an example data set.