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

Table 1

Fitted and predicted values of annual per capita electricity consumption of China (Example 1).

Year	k	Actual values	GM(1,1)		FGM(1,1)		NIPGM(1,1)		WFGM(1,1)
		2000	1	1066.9	1066.9	0.00	1066.9	0.00	1066.9	0.00	1066.9	0.00
2001	2	1157.6	1266.0	9.36	1143.0	1.26	1088.8	5.95	1111.9	3.95
2002	3	1286.0	1399.9	8.85	1314.2	2.19	1289.4	0.27	1288.0	0.15
2003	4	1477.1	1548.0	4.80	1508.2	2.10	1496.7	1.33	1490.3	0.89
2004	5	1695.2	1711.7	0.97	1714.1	1.12	1710.8	0.92	1704.9	0.57
2005	6	1913.0	1892.8	1.06	1929.4	0.86	1932.0	0.99	1928.2	0.79
2006	7	2180.6	2093.0	4.02	2153.4	1.25	2160.4	0.93	2158.9	0.99
2007	8	2482.2	2314.4	6.76	2386.1	3.87	2396.3	3.46	2396.8	3.44
2008	9	2607.6	2559.2	1.86	2627.9	0.78	2639.9	1.24	2641.7	1.31
2009	10	2781.7	2829.9	1.73	2879.3	3.51	2891.6	3.95	2893.6	4.02
2010	11	3134.8	3129.3	0.18	3140.8	0.19	3151.5	0.53	3152.8	0.57
2011	12	3497.0	3460.3	1.05	3413.0	2.40	3420.0	2.20	3419.4	2.22
2012	13	3684.2	3826.3	3.86	3696.5	0.33	3697.3	0.35	3693.5	0.25
MAPE				3.42		1.53		1.70		1.47
2013	14	3993.0	4231.1	5.96	3992.1	0.20	3983.7	0.23	3975.4	0.44
2014	15	4132.9	4678.7	13.21	4300.3	4.05	4279.5	3.55	4265.3	3.20
2015	16	4321.0	5173.6	22.28	4621.8	9.24	4585.0	8.37	4563.4	7.86
MAPE				13.82		4.44		4.05		3.83