Forecasting the volatility of EUA futures with economic policy uncertainty using the GARCH-MIDAS model

Financial Innovation

Table 4 MCS test results of the model (400-day out-of-sample prediction window)

Model	MAE		MSE		MAD		MSD		R\(^2\)LOG		QLIKE
Model	\(T_{R}\)	\(T_{SQ}\)	\(T_{R}\)	\(T_{SQ}\)	\(T_{R}\)	\(T_{SQ}\)	\(T_{R}\)	\(T_{SQ}\)	\(T_{R}\)	\(T_{SQ}\)	\(T_{R}\)	\(T_{SQ}\)
GM-\(^{\bigtriangleup }GEPU\)	0.064	0.053	0.525	0.628	0.027	0.019	0.175	0.175	0.153	0.206	0.335	0.264
GM-\(^{\bigtriangleup }EEPU\)	1.000	1.000	0.978	0.978	1.000	1.000	1.000	1.000	1.000	1.000	1.000	1.000
GARCH	0.001	0.006	0.221	0.118	0.000	0.000	0.003	0.005	0.000	0.000	0.335	0.264
GJRGARCH	0.003	0.009	0.105	0.060	0.001	0.000	0.003	0.004	0.000	0.002	0.319	0.233
NAGERCH	0.031	0.029	0.221	0.211	0.027	0.019	0.094	0.050	0.576	0.576	0.319	0.233
NGARCH	0.003	0.013	0.525	0.628	0.000	0.000	0.003	0.004	0.000	0.000	0.319	0.233
EGARCH	0.064	0.053	1.000	1.000	0.004	0.003	0.094	0.050	0.000	0.000	0.113	0.123
IGARCH	0.000	0.002	0.221	0.138	0.000	0.000	0.000	0.002	0.000	0.000	0.335	0.264