Table 10.

Model fitting results for the second type models.

Futures varieties	Mean equation	Variance equation
Copper	ARMA (1, 0)	GARCH (1, 1):${\sigma }_t^2=4.26*{10}^{-5}+4.54*{10}^{-5}*D+0.083489*{\epsilon }_{t-1}^2+0.516875*{\sigma }_{t-1}^2+2.35*{10}^{-4}*D*{\Delta }_{t-1}$
Soybean	ARMA (2, 2)	GARCH (0, 1):${\sigma }_t^2=8.32*{10}^{-5}+1.16*{10}^{-4}*D+0.12427*{\epsilon }_{t-1}^2-4.6*{10}^{-5}*D*{\Delta }_{t-1}$
Oil	ARMA (3, 3)	GARCH (0, 1):${\sigma }_t^2=3.24*{10}^{-4}+9.53*{10}^{-5}*D+0.757138*{\epsilon }_{t-1}^2-1.76*{10}^{-4}*D*{\Delta }_{t-1}$
Gold	ARMA (9, 9)	GARCH (0, 2):${\sigma }_t^2=4.72*{10}^{-5}+5.01*{10}^{-5}*D+0.033494*{\epsilon }_{t-1}^2+0.289432*{\epsilon }_{t-2}^2+9.59*{10}^{-5}*D*{\Delta }_{t-1}$