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

Table 1

Metrics of models for fitting in Case 1.

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)	(%)
1999	213.7	213.7000	0	213.7000	0	213.7000	0	213.7000	0	213.7000	0	213.7000	0	213.7000	0
2000	228.8	215.0852	−5.9942	212.7806	−7.0015	232.9317	−1.8058	208.0514	−9.0684	219.8465	3.9133	72.66238	−68.2420	231.0545	0.9854
2001	234.0	243.8493	4.2091	241.1982	3.0762	248.7854	−6.3186	230.602	−1.4522	242.3371	3.5628	95.60745	−59.1421	249.255	6.5192
2002	252.7	268.6015	6.2926	265.726	5.1547	265.7182	−5.1516	253.0378	0.1337	264.7132	4.7539	124.4687	−50.7445	268.3428	6.1903
2003	281.3	291.4472	3.6073	288.4105	2.5277	283.8034	−0.8900	275.3594	−2.1118	286.9755	2.0176	159.8201	−43.1852	288.3612	2.5102
2004	328.5	313.3144	−4.6227	310.1574	−5.5837	303.1196	7.7262	297.5674	−9.4163	309.1244	5.8982	201.6125	−38.6263	309.3555	−5.8279
2005	334.3	334.7051	0.1212	331.4585	−0.8500	323.7504	3.1557	319.6625	−4.3786	331.1607	0.9391	248.7314	−25.5963	331.3732	−0.8755
2006	359.2	355.928	−0.9109	352.6165	−1.832827	345.7855	3.73456	341.6451	−4.8872	353.0848	1.7024	298.5667	−16.8801	354.4644	−1.3184
2007	377.0	377.1903	0.0505	373.8355	−0.8394	369.3202	2.0371	363.5158	−3.5767	374.8974	0.5577	346.8195	−8.0054	378.6812	0.4459
2008	384.7	398.6414	3.6240	395.2631	2.7458	394.4568	−2.5362	385.2752	0.1495	396.599	3.0931	387.8443	0.8173	404.0787	5.0373
2009	400.6	420.3955	4.9415	417.0120	4.0969	421.3042	−5.1683	406.9239	1.5786	418.1901	4.3909	415.7108	3.7720	430.7143	7.5173
2010	455.5	442.5437	−2.8444	439.1731	−3.5844	449.9789	1.2121	428.4625	−5.9358	439.6714	3.4750	425.8055	−6.5191	458.6484	0.6912
MAPEFIT (%)			3.3835		3.3903		3.6124		3.8808		3.1185		29.2300		3.4471
2011	472.4	465.1620	−1.5322	461.8220	−2.2392	480.6053	−1.7369	449.8914	−4.7647	461.0433	2.4040	416.3413	−11.8668	487.9443	3.2905
2012	495.3	488.3161	−1.4100	485.0246	−2.0746	513.3161	−3.6374	471.2113	−4.8635	482.3065	2.6234	388.9955	−21.4626	518.6684	4.7180
2013	517.3	512.0644	−1.0121	508.8396	−1.6355	548.2533	−5.9836	492.4227	−4.8091	503.4615	2.6751	348.3102	−32.6677	550.8903	6.4934
2014	539.3	536.4604	−0.5265	533.3208	−1.1087	585.5684	−8.5793	513.5262	−4.7791	524.5088	2.7427	300.1995	−44.3354	584.6831	8.4152
2015	573.3	561.5537	−2.0489	558.5185	−2.5783	625.4232	−9.0918	534.5223	−6.7640	545.4491	4.8580	250.3389	−56.3337	620.1233	8.1673
2016	587.0	587.3918	0.0667	584.4808	−0.4292	667.9906	−13.7974	555.4115	−5.3813	566.2827	3.5293	203.0806	−65.4037	657.2912	11.9747
2017	610.7	614.0203	0.5437	611.2542	0.0907	713.4552	−16.8258	576.1944	−5.6502	587.0104	3.8791	161.089	−73.6222	696.2711	14.0120
2018	641.2	641.4836	0.0442	638.8841	−0.3612	762.0142	−18.8419	596.8716	−6.9133	607.6326	5.2351	125.5214	−80.4240	737.1513	14.9643
MAPEPRE (%)			0.8981		1.3147		9.8118		5.4906		3.4933		48.2645		9.0044