The TPCE provides a direct indication of the impact of trending errors on profit.
The methods which use all available data to fit the forecasting equations (the all-data methods) clearly stand out as the most accurate in terms of the absolute average TPCE criterion.(15) The average TPCEs for BIL are reported in Table 3.
Let X be the set of 72 BIL forecasting methods whose average absolute TPCEs are shown in Table 2, that is, X is the set of models considered in this study.(16) Let us assume that a "good" trend methodology is one that predicted well enough in the past (according to the TPCE values shown in Table 2) to be "near" the "best" method according to the Table 2 test results; namely, the method that uses linear OLS time trends with all data for frequency and an exponential time trend for severity.
In the claim cost forecasting experiments discussed above, the minimum absolute TCPE criterion would produce method 6(2) as the "best." The judgmental or "subjective intersection" of the absolute average and average TPCE criteria leads to the selection of the four "good" methods 6(7), 6(8), 11(7), and 11(8), none of which was the "best" by any single-criterion.
In order to keep the arithmetic simple, we initially use only the two "best" methods shown in Table 4 plus the method with the lowest absolute average TPCE. Our decision criteria are based on the following goals:
where Average(|TPCE.sub.x~) = the average TPCE for method x, and |U.sub.g2~(x) = the membership function of the fuzzy set of forecasts that are "good" according to the historical unbiasedness criterion (goal 2).
As an example of the FST decision-making process, we use two of the conventionally-chosen "best" methods and, for contrast, the method with the lowest TPCE in Table 2:
An insurer choosing a forecast method with the lowest TPCE will not be successful if this method consistently underestimates claim costs.
Both average absolute and average TPCEs are reported.