An Optimization Grey Bernoulli Model and Its Application in Forecasting Oil Consumption

Table 2

Metrics of models for fitting in Case 2.

Year	Raw data	ONGBM	APE	NGBM	APE	GM	APE	NGM	APE	TDGM	APE	Verhulst	APE	AR-GM	APE
		(1,1)	(%)	(1,1)	(%)	(1,1)	(%)	(1,1)	(%)	(1,1)	(%)		(%)	(1,1)	(%)
2004	12.4	12.4	0	12.4	0	12.4	0	12.4	0	12.4	0	12.4	0	12.4	0
2005	12.9	13.2328	2.5796	13.9921	8.4659	15.2246	−18.0201	7.8722	−38.9750	12.7664	1.0358	6.4967	−49.6382	14.5834	13.0500
2006	14.4	15.0446	4.4766	15.8268	9.9086	15.7179	−9.1522	13.6896	−4.9336	15.9771	10.9519	9.3351	−35.1732	15.9538	10.7902
2007	18.5	16.2433	−12.1984	16.9431	−8.4157	16.2272	12.2853	16.2658	−12.0767	17.3294	6.3274	12.7894	−30.8684	16.8138	−9.1144
2008	19.2	17.0617	−11.1369	17.6239	−8.2089	16.7530	12.7446	17.4067	−9.3400	17.8991	6.7758	16.4237	−14.4598	17.3536	−9.6166
2009	18.7	17.6170	−5.7917	18.0100	−3.6901	17.2959	7.5087	17.912	−4.2141	18.1390	3.0001	19.4232	3.8671	17.6924	−5.3884
2010	16.6	17.9785	8.3043	18.1844	9.5445	17.8563	−7.5682	18.1357	9.2513	18.2400	9.8797	20.8529	25.6197	17.9050	7.8614
2011	18.1	18.1921	0.5086	18.205	0.5609	18.4349	−1.8504	18.2348	0.7448	18.2826	1.0088	20.1871	11.5308	18.0384	−0.3402
2012	18.1	18.2896	1.0474	18.0992	−0.0042	19.0322	−5.1506	18.2787	0.9873	18.3005	1.1079	17.6770	−2.3373	18.1222	0.1225
MAPEFIT (%)			5.7554		6.0998		9.2850		10.0653		5.0109		21.6868		7.0355
2013	17.5	18.2946	4.5406	17.9052	2.3154	19.6490	−12.2798	18.2981	4.5607	18.3081	4.6176	14.1695	−19.0316	18.1747	3.8556
2014	17.0	18.2251	7.2062	17.6402	3.7660	20.2856	−19.3273	18.3067	7.6867	18.3113	7.7133	10.5746	−37.7964	18.2077	7.1042
2015	17.1	18.0949	5.8180	17.3204	1.2891	20.9430	−22.4734	18.3105	7.0792	18.3126	7.0912	7.4784	−56.2670	18.2284	6.5989
2016	18.2	17.9152	−1.5646	16.9585	−6.8215	21.6216	−18.7998	18.3122	0.6167	18.3132	0.6218	5.0897	−72.0347	18.2414	0.2275
2017	17.7	17.6952	−0.0273	16.5645	−6.4154	22.3222	−26.1140	18.313	3.46318	18.3134	3.4656	3.3742	−80.9367	18.2496	3.1049
2018	18.1	17.4421	−3.6349	16.1466	−10.7924	23.0455	−27.3231	18.3133	1.1785	18.3135	1.1796	2.1982	−87.8555	18.2547	0.8546
MAPEPRE (%)			3.7986		5.2333		21.0529		4.0975		4.1148		58.9870		3.6243