Forecasting Natural Gas Consumption in the US Power Sector by a Randomly Optimized Fractional Grey System Model

Table 3

Evaluation metrics of the forecasting models

	1-Step	2-Step	3-Step	1-Step	2-Step	3-Step	1-Step	2-Step	3-Step
	FNGM			GM			NGM
MAE	24.45	40.34	55.63	210.44	285.39	343.63	1.82 E + 12	1.91 E + 13	2.15 E + 14
MAPE	2.58%	4.17%	5.64%	21.68%	29.37%	35.44%	1.49 E + 11	1.61 E + 12	2.09 E + 13
RMSE	35.26	51.51	71.21	254.75	342.68	396.63	9.59 E + 12	1.06 E + 14	1.18 E + 15
	DGM			NDGM			FGM
MAE	208.05	282.17	340.31	1.19 E + 23	5.69 E + 26	5.23 E + 30	93.66	113.47	137.90
MAPE	21.34%	28.93%	34.98%	1.00 E + 20	5.52 E + 23	5.89 E + 27	8.68%	10.42%	12.57%
RMSE	254.33	341.44	394.63	6.71 E + 23	3.17 E + 27	2.86 E + 31	153.10	183.19	219.73
	FDGM			FNDGM			NIPGM
MAE	88.90	117.24	150.52	1.41 E + 12	1.49 E + 14	2.25 E + 16	134.41	167.94	205.14
MAPE	9.17%	12.00%	15.26%	1.13 E + 09	1.19 E + 11	1.79 E + 13	13.67%	16.81%	20.23%
RMSE	148.13	163.90	203.60	7.98 E + 12	8.30 E + 14	1.23 E + 17	172.17	214.40	261.96
	NIPNGM			NIPDGM			NIPNDGM
MAE	3.33 E + 06	1.04 E + 07	3.23 E + 07	84.82	95.12	105.74	5.36 E + 08	8.36 E + 09	1.60 E + 11
MAPE	4.15 E + 03	1.29 E + 04	4.05 E + 04	8.40%	9.34%	10.24%	7.03 E + 05	1.10 E + 07	2.10 E + 08
RMSE	1.30 E + 07	4.01 E + 07	1.24 E + 08	110.79	123.73	144.06	3.03 E + 09	4.65 E + 10	8.78 E + 11