A Multivariate Grey Prediction Model Using Neural Networks with Application to Carbon Dioxide Emissions Forecasting

Table 4

MAPE (%) obtained by different MGPMs for carbon dioxide emissions in Taiwan.

Year	Actual	GM (1, N)		TNGM (1, N)		OGM (1, N)		TDVGM (1, N)		ARIMA		The proposed MGPM
		Predicted	APE	Predicted	APE	Predicted	APE	Predicted	APE	Predicted	APE	Predicted	APE
2005	253.64	253.64	0.00	253.64	0.00	253.64	0.00	250.18	1.36	253.64	0.00	253.64	0.00
2006	260.86	220.24	15.57	260.33	0.20	260.38	0.18	250.79	3.86	255.91	1.90	261.36	0.19
2007	263.94	270.58	2.52	264.40	0.17	264.29	0.13	251.06	4.88	251.58	4.68	258.87	1.92
2008	252.75	253.11	0.14	253.18	0.17	252.48	0.11	251.24	0.60	252.39	0.14	249.56	1.26
2009	239.68	252.71	5.44	239.68	0.00	239.66	0.01	251.36	4.87	252.24	5.24	233.84	2.44
2010	256.22	256.63	0.16	255.82	0.16	256.81	0.23	251.43	1.87	252.26	1.54	250.40	2.27
2011	254.70	249.01	2.23	252.97	0.68	252.88	0.71	251.43	1.28	252.26	0.96	241.07	5.35
2012	246.55	248.41	0.75	247.71	0.47	247.24	0.28	251.37	1.95	252.26	2.32	242.89	1.48
MAPE	—	—	3.35	—	0.23	—	0.21	—	2.59	—	2.10	—	1.86
2013	253.64	251.97	1.77	254.77	2.90	257.98	4.20	251.24	1.47	252.26	1.89	249.91	0.94
2014	260.86	251.07	0.56	260.44	4.32	268.40	7.51	251.04	0.55	252.26	1.04	251.72	0.83
2015	263.94	253.13	1.50	266.89	7.02	283.29	13.60	250.77	0.56	252.26	1.15	253.15	1.51
MAPE	—	—	1.28	—	4.75	—	8.43	—	0.86	—	1.36	—	1.09