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Table 13 A comparison of alternative forecasting 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

DMSPE(1)

0.002

0.212

0.000

0.000

0.000

0.000

DMSPE(0.9)

0.267

0.487

0.000

0.026

0.000

0.001

Ridge

0.002

0.533

0.684

0.026

0.003

0.002

Lasso

0.002

0.533

0.000

0.000

0.000

0.000

Elastic net

0.002

0.487

0.000

0.000

0.000

0.000

MoJ

1.000

1.000

1.000

1.000

1.000

1.000

Panel B: 5-day horizon

DMSPE(1)

0.000

0.011

0.000

0.000

0.000

0.000

DMSPE(0.9)

0.000

0.016

0.000

0.000

0.000

0.000

Ridge

0.000

0.016

0.000

0.000

0.000

0.000

Lasso

0.000

0.016

0.000

0.000

0.000

0.000

Elastic net

0.000

0.016

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

DMSPE(1)

0.000

0.003

0.000

0.000

0.000

0.000

DMSPE(0.9)

0.000

0.003

0.000

0.000

0.000

0.000

Ridge

0.000

0.003

0.000

0.000

0.000

0.000

Lasso

0.000

0.004

0.001

0.000

0.000

0.000

Elastic net

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

DMSPE(1)

0.000

0.000

0.000

0.000

0.000

0.000

DMSPE(0.9)

0.000

0.000

0.000

0.000

0.000

0.000

Ridge

0.000

0.000

0.000

0.000

0.000

0.000

Lasso

0.000

0.000

0.000

0.000

0.000

0.000

Elastic net

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 for the MoJ and alternative models. Panels A, B, C, and D report the corresponding results for 1-day, 5-day, 10-day, and 22-day horizons, respectively. The combination models of DMSPE(1) and DMSPE(0.9) calculate the weights of the individual HAR-RV and HAR-CJ forecasts based on their past forecasting performance, while our MoJ strategy switches between the HAR-RV and HAR-CJ forecasts based on their relatively past forecasting performance. The shrinkage methods of the ridge, lasso, and elastic net are performed based on the HAR-CJ model. In the MoJ model, 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