Time-Delayed Polynomial Grey System Model with the Fractional Order Accumulation

Table 3

Numerical results by the TDPGM(1,1), GM(1,1), , and .

Year	Natural gas consumption	TDPGM(1,1)	Eror(%)	GM(1,1)	Eror(%)	TDP	Eror(%)	G	Eror(%)
1995	177.53	177.53	0	177.53	0	177.53	0	177.53	0
1996	188.05	180.88	3.81	343.87	82.86	186.45	0.85	185.64	1.28
1997	176.13	193.11	9.46	184.26	4.62	190.65	8.24	189.35	7.51
1998	218.7	206.39	5.63	204.11	6.67	215.94	1.26	207.48	5.13
1999	215.34	222.06	3.12	226.11	5.00	223.14	3.62	221.26	2.75
2000	245.03	241.61	1.40	250.47	2.22	235.75	3.79	240.34	1.91
2001	274.3	266.66	2.79	277.45	1.15	276.62	0.85	268.57	2.09
2002	291.84	299.00	2.45	307.34	5.31	289.28	0.88	305.29	4.61
2003	339.08	340.60	0.45	340.46	0.41	326.92	3.59	347.21	2.40
2004	396.72	393.61	0.79	377.14	4.94	391.64	1.28	384.94	2.97
MAPE ()			3.01		11.32		2.44		3.06
2005	467.63	460.40	1.55	417.77	10.66	451.32	3.49	448.38	4.12
2006	561.41	543.58	3.18	462.78	17.57	543.84	3.13	533.06	5.05
2007	705.23	646.00	8.40	512.64	27.31	658.56	6.62	624.31	11.47
2008	812.94	770.82	5.18	567.87	30.15	771.85	5.05	751.51	7.56
2009	895.2	921.47	2.93	629.05	29.73	876.45	2.09	867.73	3.07
2010	1069.41	1101.76	3.03	696.83	34.84	1020.62	4.56	1016.15	4.98
2011	1305.3	1315.85	0.81	771.90	40.86	1203.47	7.80	1215.32	6.89
2012	1463	1568.31	7.20	855.07	41.55	1412.62	3.44	1406.28	3.88
2013	1705.37	1864.18	9.31	947.19	44.46	1685.16	1.19	1675.61	1.75
MAPE ()			4.62		30.79		4.15		5.42