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Table 7 MCS out-of-sample test using the logarithmic HAR-RV and HAR-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

HAR-RV

0.127

0.038

0.000

0.073

0.000

0.002

HAR-CJ

0.788

0.827

0.851

1.000

0.349

0.387

Mean

1.000

0.739

0.046

0.208

0.001

0.056

MoJ

0.788

1.000

1.000

0.856

1.000

1.000

Panel B: 5-day horizon

HAR-RV

0.000

0.002

0.000

0.000

0.000

0.000

HAR-CJ

0.000

0.033

0.002

0.001

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 C: 10-day horizon

HAR-RV

0.000

0.001

0.000

0.000

0.000

0.000

HAR-CJ

0.000

0.003

0.000

0.000

0.000

0.000

Mean

0.000

0.001

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

0.000

0.000

0.000

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

  1. 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 logarithmic 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