Parameter Optimization on the Three-Parameter Whitenization Grey Model and Its Application in Simulation and Prediction of Gross Enrollment Rate of Higher Education in China

Table 1

Simulation and prediction results of different models on China’s higher education gross enrollment rate.

Serial number		TWGM(1,1|0.5,1)		TWGM(1,1|0.5,r∗)		TWGM()		TWGM()
		Simulation data
k = 2	3.5	3.14	10.2188	3.13	10.6725	3.15	10.1019	3.10	11.5502
k = 3	3.9	4.04	3.5078	4.06	4.1620	4.04	3.6783	4.05	3.7288
k = 4	5	4.97	0.6278	5.00	0.0311	4.98	0.4414	4.98	0.4818
k = 5	6	5.94	1.0113	5.96	0.6118	5.95	0.8097	5.93	1.1729
k = 6	7.2	6.95	3.4645	6.96	3.2806	6.97	3.2561	6.92	3.9439
k = 7	8.3	8.00	3.5661	8.00	3.5641	8.02	3.3488	7.94	4.3312
k = 8	9.1	9.10	0.0159	9.09	0.1324	9.12	0.2488	9.01	1.0183
k = 9	9.8	10.24	4.5378	10.22	4.2692	10.27	4.7877	10.12	3.2693
k = 10	10.5	11.44	8.9113	11.40	8.5588	11.46	9.1774	11.28	7.4608
k = 11	12.5	12.68	1.4111	12.63	1.0562	12.71	1.6634	12.50	0.0000
k = 12	13.3	13.97	5.0293	13.92	4.6743	14.00	5.2945	13.77	3.5632
k = 13	15	15.32	2.1024	15.27	1.8063	15.35	2.3637	15.11	0.7258
k = 14	17	16.72	1.6586	16.68	1.8634	16.76	1.4040	16.51	2.8898
k = 15	19	18.18	4.3196	18.16	4.4102	18.23	4.0694	17.98	5.3818
k = 16	21	19.70	6.1832	19.71	6.1376	19.75	5.9357	19.52	7.0515
k = 17	22	21.29	3.2394	21.33	3.0264	21.34	2.9821	21.14	3.9173
k = 18	23	22.94	0.2639	23.04	0.1533	23.00	0.0032	22.84	0.7002
k = 19	23.3	24.66	5.8381	24.82	6.5170	24.73	6.1234	24.63	5.6917
Forecast data
k = 20	24.2	26.45	9.3103	26.69	10.2816	26.52	9.6068	26.50	9.5236
k = 21	26.5	28.32	6.8708	28.65	8.1088	28.40	7.1623	28.48	7.4706
k = 22	26.9	30.27	12.5146	30.71	14.1460	30.35	12.8231	30.56	13.5932
k = 23	30	32.29	7.6443	32.86	9.5415	32.38	7.9409	32.74	9.1365
k = 24	34.5	34.40	0.2759	35.13	1.8131	34.50	0.0000	35.04	1.5616
k = 25	37.5	36.60	2.3881	37.50	0.0000	36.71	2.1169	37.46	0.1167
k = 26	40	38.90	2.7601	39.99	0.0210	39.00	2.4889	40.00	0.0000
k = 27	42.7	41.28	3.3183	42.61	0.2195	41.40	3.0476	42.68	0.0541
k = 28	45.7	43.77	4.2234	45.35	0.7650	43.89	3.9543	45.49	0.4502
k = 29	48.1	46.36	3.6163	48.23	0.2714	46.49	3.3446	48.46	0.7477
k = 30	51.6	49.06	4.9237	51.25	0.6712	49.20	4.6548	51.58	0.0365