Research on the Influence of Volatility of International Energy Commodity Futures Market on CPI in China

Table 5

The goodness of fit and prediction accuracy at the optimal lag order of each cross-multiplication variable.

Model	Index	CRB × coal	NH × coal	Exchange × coal	CRB × NH	CRB × exchange
		Lag = 36	Lag = 24	Lag = 22	Lag = 37	Lag = 24
Beta-MIDAS	R^2	0.8652	0.8602	0.8696	0.8740	0.8657
	RMSE	0.5542	0.5567	0.6349	0.6626	0.6733
	MSFE	0.3072	0.3100	0.4031	0.4390	0.4534
	DMSFE	0.0882	0.0901	0.1044	0.1017	0.1099
Beta-nonzero-MIDAS	R^2	0.8668	0.8582	0.8598	0.8735	0.8665
	RMSE	0.5792	0.5502	0.5404	0.6665	0.6772
	MSFE	0.3355	0.3028	0.2921	0.4442	0.4586
	DMSFE	0.0947	0.0893	0.0853	0.1018	0.1116
Exp Almon-MIDAS	R^2	0.8659	0.8615	0.8706	0.8742	0.8659
	RMSE	0.5222	0.5662	0.6259	0.6646	0.6794
	MSFE	0.2727	0.3206	0.3917	0.4417	0.4616
	DMSFE	0.0837	0.0920	0.1034	0.1024	0.1111
U-MIDAS	R^2	0.9316	0.9095	0.9070	0.9220	0.9020
	RMSE	0.5205	0.5288	0.5906	0.8027	0.8192
	MSFE	0.2710	0.2796	0.3488	0.6443	0.6711
	DMSFE	0.0626	0.0769	0.0981	0.1264	0.1475
Stepfun-MIDAS	R^2	0.9096	0.8919	0.8907	0.8940	0.8868
	RMSE	0.5118	0.4745	0.4944	0.7087	0.7423
	MSFE	0.2619	0.2252	0.2444	0.5022	0.5509
	DMSFE	0.0742	0.0722	0.0798	0.1295	0.1378
Almon-MIDAS	R^2	0.9043	0.8870	0.8885	0.8778	0.8731
	RMSE	0.4911	0.4863	0.5091	0.6344	0.5910
	MSFE	0.2412	0.2365	0.2592	0.4024	0.3493
	DMSFE	0.0613	0.0679	0.0809	0.1054	0.0933