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Table 5 MCS out-of-sample forecasting test using the HAR-TCJ jump model

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

0.489

0.046

0.001

0.010

0.000

0.001

HAR-TCJ

0.291

1.000

1.000

0.010

0.040

0.019

Mean

0.568

0.640

0.014

0.010

0.000

0.002

MoJ

1.000

0.640

0.247

1.000

1.000

1.000

Panel B: 5-day horizon

HAR-RV

0.000

0.003

0.000

0.004

0.000

0.000

HAR-TCJ

0.000

1.000

0.039

0.027

0.000

0.000

Mean

0.000

0.188

0.000

0.004

0.000

0.000

MoJ

1.000

0.998

1.000

1.000

1.000

1.000

Panel C: 10-day horizon

HAR-RV

0.000

0.000

0.000

0.005

0.000

0.000

HAR-TCJ

0.000

0.209

0.000

0.009

0.000

0.000

Mean

0.000

0.004

0.000

0.005

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

0.001

0.000

0.006

0.000

0.000

HAR-TCJ

0.000

0.055

0.000

0.006

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

  1. 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-TCJ forecasts, while our MoJ strategy switches between the HAR-RV and HAR-TCJ 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