A Seemingly Unrelated Regression Model With MA Error Structure In Credibility Framework

Credibility theory is a technique for predicting future claims of a risk class, given past claims of that and related risk classes. The first credibility regression model appeared in Hachmemeister's paper in 1975. Since then, it has been greatly developed.One of these extensions is a credibility model with seemingly unrelated regression (SUR) by Georgios Pitselis in 2004. To estimate individual premium by using data with cross-section and time effects, he transplanted the idea of Zeller's (1962) SUR model to construct a SUR credibility model and established unbiased credibility estimators for it. It is well known, in Zellner's model the correlations of contemporaneous disturbance terms in different regression equations are considered and the estimators is proved to be at least asymptotically more efficient than single-equation least squares. However, the correlation effect over time in SUR model is not taken into account.In a standard linear model, we often assume the error terms are identically independent distributed. In fact people usually find some pattern of correlation exists when observing an object repeatedly. If he takes into account the correlation effect in the model, the GLS estimator of regression coefficient is more efficient than OLS estimator. Therefore, in this case, credibility type estimators based on GLS estimators are better than those based on OLS estimators.Due to these thinking, the aim of this paper is to establish a SUR credibility model with an additional MA error structure and consequently deduce the credibility estimators as well as a method to estimate unknown structural parameters. Finally, a simulation is preformed to evaluate the goodness of the estimators.