RMSEs of the prediction using models Eq (9) and Eq (10) respectively of different hypotheses when considering tail events (Extreme 0.1%, 1% and 2%) and all cases.

The rows indicate the responses (loss and absolute return). Each RMSE of the predictive models in H1a, H1b and H2 is compared with the RMSE of the predictive model in H0, using respectively the same data with the sets of time indexes Q(99.9), Q(99) and Q(98). The values inside the brackets are the percentage differences of the RMSE of the model in H1a, H1b or H2 to the RMSE of the model in H0. A negative percentage means that the model under the alternative hypothesis has a smaller RMSE, i.e., the model under the alternative hypothesis performs better.