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

Table 3

Metrics of models for fitting in Case 3.

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	87.1	87.1	0	87.1	0	87.1	0	87.1	0	87.1	0	87.1	0	87.1	0
2000	91.2	81.9017	−10.1955	80.1035	−12.1672	89.1865	2.2078	84.6546	−7.1770	88.4599	3.0045	24.3087	−73.3457	89.4691	−1.8980
2001	89.7	87.9096	−1.9960	86.1203	−3.9907	89.7028	−0.0031	85.8011	−4.3466	89.3157	0.4284	30.4944	−66.0040	90.9500	1.3935
2002	85.7	91.5129	6.7828	89.8657	4.8608	90.2221	−5.2766	86.8598	1.3534	90.1060	5.1412	37.8939	−55.7830	91.8757	7.2062
2003	88.0	93.7467	6.5304	92.3067	4.8940	90.7444	−3.1186	87.8376	−0.1845	90.8359	3.2226	46.5390	−47.1148	92.4545	5.0619
2004	91.6	95.0866	3.8063	93.8903	2.5003	91.2697	0.3606	88.7406	−3.1216	91.5099	0.0984	56.3387	−38.4948	92.8162	1.3277
2005	93.8	95.7964	2.1284	94.8653	1.1357	91.7981	2.1342	89.5745	−4.5048	92.1323	1.7779	67.0245	−28.5453	93.0424	−0.8077
2006	92.8	96.0402	3.4916	95.3867	2.7874	92.3295	0.5070	90.3447	−2.6458	92.7071	0.1001	78.1046	−15.8355	93.1837	0.4135
2007	96.4	95.9279	−0.4897	95.5584	−0.8731	92.8640	3.6680	91.0559	−5.5437	93.2379	3.2802	88.8524	−7.8294	93.2721	−3.2447
2008	96.2	95.5373	−0.6888	95.4540	−0.7755	93.4017	2.9089	91.7127	−4.6645	93.7280	2.5696	98.3542	2.2392	93.3273	−2.9861
2009	92.9	94.9256	2.1804	95.1278	2.3981	93.9424	−1.1220	92.3193	−0.6251	94.1807	1.3785	105.6322	13.7053	93.3619	0.4972
2010	93.3	94.1363	0.8964	94.6212	1.4161	94.4862	−1.2714	92.8795	−0.4507	94.5987	1.3919	109.8311	17.7182	93.3834	0.0894
2011	94.9	93.2032	−1.7880	93.9663	−0.9838	95.0332	−0.1404	93.3968	−1.5840	94.9847	0.0892	110.4153	16.3491	93.3969	−1.5838
2012	96.4	92.1533	−4.4053	93.1889	−3.3310	95.5834	0.8471	93.8746	−2.6198	95.3412	1.0984	107.3079	11.3153	93.4054	−3.1065
2013	93.8	91.0081	−2.9764	92.3096	−1.5889	96.1367	−2.4912	94.3158	0.5499	95.6704	1.9940	100.9113	7.5813	93.4107	−0.4151
MAPEFIT (%)			3.4540		3.1216		1.8612		2.8122		1.8268		28.7044		2.1451
2014	89.5	89.7856	0.3191	91.3456	2.0621	96.6933	−8.0372	94.7232	5.8360	95.9744	7.2339	92.0010	2.7944	93.4139	4.3731
2015	88.5	88.5004	0.0004	90.3111	2.0464	97.2530	−9.8904	95.0995	7.4571	96.2551	8.7628	81.5382	−7.8665	93.4160	5.5548
2016	89.1	87.1648	−2.1720	89.2179	0.1323	97.8160	−9.7823	95.4470	7.1235	96.5143	8.3214	70.4734	−20.9052	93.4173	4.8454
2017	85.8	85.7891	−0.0127	88.0761	2.6528	98.3823	−14.6647	95.7680	11.6177	96.7538	12.7666	59.6004	−30.5357	93.4181	8.8789
2018	82.8	84.3822	1.9108	86.8944	4.9449	98.9519	−19.5071	96.0643	16.0197	96.9748	17.1194	49.4852	−40.2353	93.4186	12.8244
MAPEPRE (%)			0.8830		2.3677		12.3763		9.6108		10.8408		20.4674		7.2953