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Table 10 MCS out-of-sample forecasting test based the volatility measure of realized kernel

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-RK

0.016

0.030

0.003

0.001

0.000

0.000

HAR-CJ

0.253

1.000

0.258

0.001

0.000

0.000

Mean

0.253

0.170

0.042

0.001

0.000

0.000

MoJ

1.000

0.489

1.000

1.000

1.000

1.000

Panel B: 5-day horizon

HAR-RK

0.000

0.012

0.000

0.000

0.000

0.000

HAR-CJ

0.000

0.012

0.000

0.000

0.000

0.000

Mean

0.000

0.012

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-RK

0.000

0.003

0.000

0.000

0.001

0.001

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-RK

0.000

0.003

0.000

0.015

0.000

0.000

HAR-CJ

0.000

0.032

0.000

0.006

0.000

0.000

Mean

0.000

0.004

0.000

0.006

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. The volatility estimator to forecast in this table is the realized kernel (RK) instead of the realized variance (RV). 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-RK and HAR-CJ forecasts, while our MoJ strategy switches between the HAR-RK 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