Multistep Wind Speed Forecasting Using a Novel Model Hybridizing Singular Spectrum Analysis, Modified Intelligent Optimization, and Rolling Elman Neural Network

Table 7

Performance evaluations of different models for the forecast of the 10 min wind speed series from the wind observation site C.

	Error	ARIMA	BPNN	RENN	SSA-RENN	SSA-PSO-RENN	Proposed model		ARIMA	BPNN	RENN	SSA-RENN	SSA-PSO-RENN	Proposed model
Spring
1-step	MSE (m/s)	0.9886	0.933	0.91	0.3511	0.3455	0.3409	2-step	1.3418	1.2772	1.174	0.5605	0.5547	0.554
	MAE (m/s)	0.7739	0.7637	0.7531	0.4734	0.4693	0.4653		0.9002	0.888	0.8637	0.5905	0.5876	0.5863
	MAPE (%)	7.79	7.48	7.39	4.67	4.63	4.59		9.1	8.8	8.53	5.86	5.83	5.82
3-step	MSE (m/s)	1.6737	1.5485	1.3948	0.8204	0.8221	0.8228	5-step	2.0057	1.8882	1.6584	1.1905	1.2223	1.2007
	MAE (m/s)	0.9984	0.9769	0.9369	0.7053	0.707	0.7051		1.1032	1.082	1.0265	0.8535	0.8653	0.8552
	MAPE (%)	10.19	9.78	9.33	7.06	7.07	7.08		11.25	10.87	10.22	8.54	8.63	8.62
Summer
1-step	MSE (m/s)	0.3861	0.3647	0.386	0.1246	0.1176	0.1108	2-step	0.6725	0.5137	0.5217	0.2596	0.2526	0.2337
	MAE (m/s)	0.497	0.4851	0.4957	0.2842	0.2808	0.2711		0.6467	0.5523	0.5614	0.3861	0.3873	0.3699
	MAPE (%)	7.82	7.23	7.36	4.23	4.18	4.1		10.47	8.19	8.31	5.61	5.6	5.46
3-step	MSE (m/s)	0.7203	0.6296	0.6273	0.4256	0.4323	0.4018	5-step	1.0697	0.8304	0.8011	0.7011	0.7408	0.6927
	MAE (m/s)	0.6478	0.6144	0.6143	0.4859	0.4911	0.4734		0.8047	0.6966	0.6876	0.6181	0.6331	0.614
	MAPE (%)	10.61	9.04	9.05	6.99	7.02	6.9		13.26	10.06	9.99	8.78	8.92	8.77
Fall
1-step	MSE (m/s)	0.0878	0.2985	0.4265	0.1268	0.1208	0.1185	2-step	0.1023	0.4189	0.447	0.2122	0.2017	0.2025
	MAE (m/s)	0.2676	0.3903	0.5267	0.2743	0.2709	0.268		0.2534	0.4647	0.5428	0.3454	0.3427	0.3413
	MAPE (%)	5.81	5.81	9.53	4.07	4.03	4		5.52	6.85	9.83	5.12	5.09	5.07
3-step	MSE (m/s)	0.1209	0.5499	0.4602	0.3148	0.3045	0.31	5-step	0.1455	0.7512	0.4765	0.4895	0.4849	0.4991
	MAE (m/s)	0.272	0.5365	0.5519	0.4118	0.4086	0.4119		0.2962	0.6405	0.5586	0.5204	0.512	0.5201
	MAPE (%)	5.94	7.87	10	6.09	6.03	6.09		6.51	9.31	10.16	7.74	7.56	7.69
Winter
1-step	MSE (m/s)	0.5355	0.7541	0.5705	0.3163	0.3245	0.3254	2-step	0.8343	1.001	0.8674	0.5561	0.568	0.5674
	MAE (m/s)	0.5268	0.6375	0.5552	0.424	0.4251	0.4244		0.643	0.729	0.6783	0.532	0.5407	0.5353
	MAPE (%)	9.56	11.75	10.35	7.88	7.87	7.82		11.6	13.37	12.66	9.76	9.97	9.73
3-step	MSE (m/s)	1.1368	1.2756	1.1347	0.8115	0.8161	0.8175	5-step	1.7051	1.7882	1.5878	1.3017	1.2785	1.2866
	MAE (m/s)	0.742	0.8183	0.7725	0.6307	0.6403	0.6351		0.9113	0.9635	0.903	0.7998	0.8049	0.7989
	MAPE (%)	13.23	14.94	14.35	11.52	11.77	11.49		15.99	17.31	16.5	14.74	14.87	14.53