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

Table 4

Metrics of models for fitting in Case 4.

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)	(%)
2008	208.2061	208.2	0	208.2	0	208.2061	0	208.2061	0	208.2061	0	208.2	0	208.2061	0
2009	210.516	211.2094	0.3370	207.897	−1.2366	211.3859	−0.4132	157.4182	−25.2227	209.8949	0.2951	159.7675	−24.1010	215.0505	2.1540
2010	211.032	218.3389	3.4781	216.5369	2.6241	213.9545	−1.3848	187.5574	−11.1237	215.0468	1.9024	219.7777	4.1600	215.3288	2.0361
2011	224.8901	218.4848	−2.8525	218.4805	−2.8544	216.5543	3.7066	203.2692	−9.6140	217.6672	3.2118	241.2857	7.2858	215.3401	−4.2465
2012	214.6511	215.0810	0.1775	216.9167	1.0325	219.1857	−2.1125	211.4598	−1.4868	219.0000	2.0260	207.317	−3.4387	215.3406	0.3212
MAPEFIT (%)			1.7113		1.9369		1.9043		11.8618		1.8588		9.7464		2.1894
2014	204.0364	209.6452	2.7672	213.2665	4.5424	221.8490	−8.7301	215.7296	5.7310	219.6779	7.6660	143.8108	−29.5045	215.3406	5.5403
2015	196.5073	202.9962	3.3059	208.3029	6.0065	224.5448	−14.2679	217.9555	10.9147	220.0227	11.9667	85.5894	−56.4431	215.3406	9.5840
2016	190.96	195.6266	2.4223	202.4959	6.0188	227.2733	−19.0162	219.1159	14.7444	220.1980	15.3111	46.3702	−75.7224	215.3406	12.7674
2017	187.8064	187.8537	0.0286	196.1525	4.4475	230.0349	−22.4852	219.7208	16.9933	220.2872	17.2949	23.8493	−87.3007	215.3406	14.6610
2018	182.3648	179.8905	−1.3758	189.4826	3.8830	232.8301	−27.6727	220.0361	20.6571	220.3326	20.8197	11.9385	−93.4548	215.3406	18.0823
MAPEPRE (%)			1.9800		4.9797		18.4344		13.8081		14.6117		68.4851		12.1270