A Novel Weighted Fractional GM(1,1) Model and Its Applications

Table 5

Fitted and predicted values of natural gas consumption of China (Example 3).

Year	k	Actual values	GM(1,1)		FGM(1,1)		NIPGM(1,1)		WFGM(1,1)
		2003	1	35	35.0	0.00	35.0	0.00	35.0	0.00	35.0	0.00
2004	2	41.5	43.7	5.22	41.6	0.31	41.5	0.00	41.5	0.00
2005	3	49.3	50.3	2.03	50.6	2.70	50.3	2.05	50.6	2.70
2006	4	58.6	57.9	1.12	59.6	1.71	59.3	1.14	59.8	2.00
2007	5	69.2	66.7	3.55	68.5	1.06	68.4	1.19	68.7	0.74
2008	6	80.3	76.9	4.25	77.3	3.74	77.6	3.12	77.3	3.69
2009	7	85.2	88.6	3.95	86.2	1.13	87.1	2.17	85.8	0.60
MAPE				2.87		1.52		1.41		1.39
2010	8	94.8	102.2	7.61	95.1	0.35	96.6	1.92	93.8	1.03
2011	9	103.1	117.5	13.98	104.2	1.10	106.3	3.15	101.7	1.38
2012	10	107.2	135.4	26.28	113.5	5.90	116.2	8.43	109.2	1.94
2013	11	119.3	155.9	30.71	123.0	3.12	126.3	5.86	116.6	2.23
MAPE				19.65		2.62		4.84		1.65