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

Financial Innovation

Table 8 MCS out-of-sample test using the square-root HAR-RV and HAR-CJ models

Models	QLIKE	MSE	MAE	MSPE	MAPE	MSE-LOG
Panel A: 1-day horizon
HAR-RV	0.118	0.040	0.000	0.055	0.000	0.001
HAR-CJ	0.436	0.317	0.604	0.669	0.098	0.061
Mean	0.436	0.139	0.004	0.091	0.000	0.001
MoJ	1.000	1.000	1.000	1.000	1.000	1.000
Panel B: 5-day horizon
HAR-RV	0.000	0.004	0.000	0.003	0.000	0.000
HAR-CJ	0.005	0.032	0.011	0.026	0.000	0.001
Mean	0.000	0.004	0.000	0.003	0.000	0.000
MoJ	1.000	1.000	1.000	1.000	1.000	1.000
Panel C: 10-day horizon
HAR-RV	0.000	0.001	0.000	0.004	0.000	0.000
HAR-CJ	0.005	0.041	0.002	0.013	0.000	0.001
Mean	0.000	0.001	0.000	0.004	0.000	0.000
MoJ	1.000	1.000	1.000	1.000	1.000	1.000
Panel D: 22-day horizon
HAR-RV	0.000	0.004	0.000	0.002	0.000	0.000
HAR-CJ	0.000	0.004	0.000	0.002	0.000	0.000
Mean	0.000	0.001	0.000	0.001	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. Particularly, the HAR-RV and HAR-CJ models used in this table are cast in standard deviation form. 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-CJ forecasts, while our MoJ strategy switches between the HAR-RV and HAR-CJ 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