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

Financial Innovation

Table 2 Out-of-sample forecasting performance based on the MCS test

Models	QLIKE	MSE	MAE	MSPE	MAPE	MSE-LOG
Panel A: 1-day horizon
HAR-RV	0.306	0.105	0.005	0.018	0.001	0.001
HAR-CJ	0.075	0.389	0.301	0.018	0.001	0.001
Mean	0.306	0.276	0.022	0.018	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	0.007	0.001	0.000	0.001	0.000
HAR-CJ	0.000	0.007	0.001	0.000	0.000	0.000
Mean	0.000	0.007	0.001	0.000	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	0.003	0.000	0.000	0.001	0.002
HAR-CJ	0.000	0.003	0.000	0.000	0.000	0.000
Mean	0.000	0.003	0.000	0.000	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	0.000	0.000	0.032	0.001	0.001
HAR-CJ	0.000	0.000	0.000	0.000	0.000	0.000
Mean	0.000	0.000	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-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. The entire sample period consisting of 1619 observations spans January 3, 2012 to May 11, 2018, while the out-of-sample forecasting period contains the last 800 observations