Table 1.

Fitting and predicting accuracy test results of typical and proposed GM(1,1) models: Eqs. (20) and (21).

k	True value	Typical GM(1,1)			OB-WMSE-GM(1,1)
		Calculated value	AE	APE (%)	Calculated value	AE	APE (%)
1	1.349859	1.349859	0.000000	0.000000	1.349859	0.000000	0.000000
2	1.822119	1.806459	0.015660	0.859415	1.824148	0.002029	0.111358
3	2.459603	2.433033	0.026570	1.080246	2.461244	0.001641	0.066721
4	3.320117	3.276936	0.043181	1.300585	3.320851	0.000734	0.022105
5	4.481689	4.413548	0.068141	1.520432	4.480681	0.001008	0.022492
6	6.049647	5.944396	0.105251	1.739791	6.045590	0.004057	0.067069
7	8.166170	8.006222	0.159948	1.958660	8.157054	0.009116	0.111626
8	11.023176	10.783197	0.239979	2.177042	11.005962	0.017214	0.156163
9	14.879732	14.523371	0.356360	2.394938	14.849871	0.029861	0.200680
10	20.085537	19.560833	0.524704	2.612348	20.036292	0.049245	0.245178
11	27.112639	26.345548	0.767091	2.829274	27.034106	0.078533	0.289655
12	36.598234	35.483556	1.114679	3.045717	36.475955	0.122279	0.334113
13	49.402449	47.791101	1.611349	3.261677	49.215436	0.187013	0.378551
14	66.686331	64.367543	2.318788	3.477157	66.404269	0.282062	0.422969