Statistical tests are developed for comparing performances of forecasting expectiles and quantiles of a random variable under consistent loss (scoring) functions. Kolmogorov-Smirnov’s type test statistics are constructed by using the extremal consistent loss functions. The null hypothesis of the tests is that a benchmark forecast performs at least equally well as a competitive one under all extremal consistent loss functions. It can be shown that if such a null hypothesis holds, the benchmark will also perform at least equally well as the competitor under all consistent loss functions. Thus, under the null hypothesis, when different 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.
The 1st International Conference on Econometrics and Statistics (HKUST), Hong Kong University of Science and Technology (HKUST) Business School EcoSta 2017 , Parallel Session F, Friday 16.06.2017 08:30 - 09:50, EG029 Room LSK1034 CONTRIBUTIONS IN FORECASTING ECONOMIC AND FINANCIAL TIME SERIES, EC0655