Skip to main content

Table 9 MCS out-of-sample test based on the MIDAS-RV and MIDAS-CJ models

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

Models

QLIKE

MSE

MAE

MSPE

MAPE

MSE-LOG

Panel A: 1-day horizon

MIDAS-RV

0.259

0.067

0.002

0.002

0.000

0.000

MIDAS-CJ

0.027

0.152

0.024

0.002

0.000

0.000

Mean

0.259

0.137

0.002

0.002

0.000

0.000

MoJ

1.000

1.000

1.000

1.000

1.000

1.000

Panel B: 5-day horizon

MIDAS-RV

0.000

0.002

0.000

0.003

0.000

0.000

MIDAS-CJ

0.000

0.002

0.000

0.000

0.000

0.000

Mean

0.000

0.002

0.000

0.000

0.000

0.000

MoJ

1.000

1.000

1.000

1.000

1.000

1.000

Panel C: 10-day horizon

MIDAS-RV

0.000

0.000

0.000

0.011

0.000

0.000

MIDAS-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

Panel D: 22-day horizon

MIDAS-RV

0.000

0.012

0.000

0.028

0.000

0.001

MIDAS-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

  1. This table provides the MCS p values of the four used models. Particularly, we use the MIDAS-RV and MIDAS-CJ models to replace the HAR-RV and HAR-CJ models, respectively. 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 MIDAS-RV and MIDAS-CJ forecasts, while our MoJ strategy switches between the MIDAS-RV and MIDAS-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