For the calendar effects, for example the January, Friday and the turn of the month effect, Sullivan et al. (2001) find that the RC in all periods does not reject the null hypothesis that the best forecasting rule encountered in the specification search does not have superior predictive ability over the buy-and-hold benchmark. If no correction were made for the specification search, then in both papers the conclusion would have been that the best model would have significant superior forecasting power over the benchmark. Hence Sullivan et al. (1999, 2000) conclude that it is very important to correct for data snooping for otherwise one can make wrong inferences about the significance of the best model found.
Hansen (2001) identifies a similarity condition for asymptotic tests of composite hypotheses, shows that this condition is a necessary condition for a test to be unbiased. He shows that White's RC does not satisfy this condition. This causes the RC to be an asymptotically biased test, which yields inconsistent p-values. Moreover, the test is sensitive to the inclusion of poor and irrelevant models in the comparison. Further, the test has poor power properties. Therefore, within the framework of White (2000), he applies the similarity condition to derive a test for superior predictive ability (SPA). The null hypothesis of this test is that none of the alternative models in the specification search is superior to the benchmark model, or stated differently, the benchmark model is not inferior to any alternative model. The alternative is that one or more of the alternative models are superior to the benchmark model. Hansen (2001) uses the RC and the SPA-test to evaluate forecasting models applied to US annual inflation in the period 1952-2000. He shows that the null hypothesis is neither rejected by the SPA-test p-value, nor by the RC p-value, but that there is a large difference between both p-values, likely to be caused by poor models in the space of forecasting models.
Grandia (2002) utilizes in his master's thesis the RC and the SPA-test to evaluate the forecasting ability of a large set of technical trading strategies applied to stocks quoted at the Amsterdam Stock Exchange in the period January 1973 through December 2001. He finds that the best trading strategy out of the set of filters, moving averages and trading range break-out rules can generate excess profits over the buy-and-hold even in the presence of transaction costs, but is not superior to the buy-and-hold benchmark after correction for the specification search. The results are stable across the subperiods 1973-1986 and 1987-2001.