To jump or not to jump: momentum of jumps in crude oil price volatility prediction

Financial Innovation

Table 4 MCS out-of-sample forecasting test using the HAR-J jump model

Models	QLIKE	MSE	MAE	MSPE	MAPE	MSE-LOG
Panel A: 1-day horizon
HAR-RV	0.079	0.026	0.000	0.032	0.000	0.000
HAR-J	0.566	0.434	1.000	0.736	0.309	0.171
Mean	0.875	0.063	0.004	0.075	0.000	0.080
MoJ	1.000	1.000	0.852	1.000	1.000	1.000
Panel B: 5-day horizon
HAR-RV	0.014	0.125	0.011	0.038	0.010	0.013
HAR-J	0.032	1.000	0.855	0.064	0.044	0.022
Mean	0.014	0.235	0.211	0.038	0.010	0.013
MoJ	1.000	0.754	1.000	1.000	1.000	1.000
Panel C: 10-day horizon
HAR-RV	0.003	0.021	0.003	0.005	0.001	0.002
HAR-J	0.005	0.250	0.013	0.005	0.001	0.002
Mean	0.001	0.021	0.001	0.005	0.000	0.001
MoJ	1.000	1.000	1.000	1.000	1.000	1.000
Panel D: 22-day horizon
HAR-RV	0.001	0.071	0.000	0.000	0.002	0.004
HAR-J	0.000	0.071	0.000	0.000	0.000	0.000
Mean	0.000	0.031	0.000	0.000	0.000	0.000
MoJ	1.000	1.000	1.000	1.000	1.000	1.000

This table provides the MCS p values of the four used models. Panels A, B, C, and D report the corresponding results for 1-day, 5-day, 10-day, and 22-day horizons, respectively. The mean combination uses the equally weighted average (that is, simple mean) of the individual HAR-RV and HAR-J forecasts, while our MoJ strategy switches between the HAR-RV and HAR-J forecasts based on their relatively past forecasting performance. The past forecasting performance is evaluated by a 5-day look-back period. The six considered loss functions are QLIKE, MSE, MAE, MSPE, MAPE, and MSE-LOG. Bold numbers highlight important instances in which the corresponding model falls into the MCS with the 10% significance level