Credibility-Weighted Trend Factors

The credibility of trend lines is important because trend lines cannot be extrapolated reliably far into the future. Credibility-weighted trend factors can be calculated if two or more alternative assumptions are considered. The effects of changes in the goodness of fit of the trend lines being considered can also be explored. This paper approaches the problem by as hoc blending of alternative sets of hypotheses. The appropriateness of the method is argued by analogy with Empirical Bayesian credibility formulas. A specific example is used throughout. In this example, a particular pair of alternative assumptions is considered - that there is no trend and that there is linear trend. The results suggest that an increase in the R2 of the linear trend line may imply an increase in the credibility of the trend line, reliance on a greater amount of trend, or a more reliable resulting estimate. Which of these or which combination of these in the case depends on the data at hand. A greater R2 does not necessarily imply greater credibility for trend. The methods shown in this paper can be extended to other sets of assumptions, and other questions about the appropriateness of trend assumptions can also be studied. LOB-Workers Comp