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

Table 2

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

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	5357.7	5357.7	0.00	5357.7	0.00	5357.7	0.00	5435.9	1.32	5357.71	0.00	5357.7	0.00
2006	5912.0	5007.9	15.29	5869.3	0.72	5912.1	0.00	5786.9	2.12	5916.89	0.08	5919.4	0.13
2007	6468.3	6941.3	7.31	6478.3	0.15	6467.7	0.01	6160.3	4.76	6437.24	0.48	6850.5	5.91
2008	6608.1	6753.8	2.20	6495.6	1.70	6609.7	0.02	6551.9	0.85	6919.37	4.71	6739.0	1.98
2009	7025.8	7003.8	0.31	7083.0	0.81	7023.3	0.04	6962.3	0.90	7366.09	4.84	7026.6	0.01
2010	7706.7	7651.5	0.72	7703.0	0.05	7709.3	0.03	7390.9	4.10	7779.98	0.95	7556.9	1.94
2011	8465.6	8429.1	0.43	8255.0	2.49	8464.0	0.02	7838.3	7.41	8163.48	3.57	8186.0	3.30
2012	8620.6	8660.7	0.47	8665.3	0.52	8621.1	0.01	8303.9	3.67	8518.80	1.18	8582.9	0.44
MAPE	—	—	3.34	—	0.81	—	0.02	—	3.14	—	1.98	—	1.71
2013	8995.8	9039.7	0.49	9011.6	0.18	9080.8	0.94	8788.2	2.31	8848.02	1.64	8990.6	0.06
2014	9036.5	9248.2	2.34	9270.5	2.59	9282.2	2.72	9290.3	2.81	9153.05	1.29	9242.6	2.28
2015	9040.7	9342.8	3.34	9452.7	4.56	9419.1	4.19	9809.9	8.51	9435.68	4.37	9335.2	3.26
MAPE	—	—	2.06	—	2.44	—	2.62	—	4.54	—	2.43	—	1.87