We develop statistical tests for comparing performances of forecasting expectiles and quantiles of a random variable under consistent loss (scoring) functions. The test statistics are constructed by using the extremal consistent loss functions of Ehm et al. (2016) and in Kolmogorov-Smirnov type. The null hypothesis of the tests is that a benchmark forecast at least performs equally well as a competitive one under all extremal consistent loss functions. It can be shown that if such a null holds, the benchmark will also perform at least equally well as the competitor under all consistent loss functions. Thus under the null, when di erent consistent loss functions are used, the result that the competitor does not outperform the benchmark will not be altered. We propose to use the re-centered bootstrap to construct empirical distributions of the proposed test statistics. Through simulations, we show the proposed test statistics perform reasonably well. We apply the proposed test on re-examining abilities of some predictors on forecasting risk premium of the S&P500 index.
2017 European meeting of the Econometric society, University of Lisbon Session 313: Inference in Forecasting, August 23, 2017 16:30 to 17:45 , C4.02, ed. II