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

Table 11

Performance evaluations of different models for the forecast of the one-hour wind speed series.

	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)	5.1762	4.5464	4.8944	1.6948	1.7761	1.5977	2-step	6.9013	5.7573	6.2777	2.6703	2.9233	2.3518
	MAE (m/s)	1.8581	1.6491	1.7513	0.9221	0.9017	0.901		2.1454	1.8997	2.0602	1.1652	1.2252	1.0835
	MAPE (%)	16.8	16.74	17.32	8.93	8.75	8.7		20.99	20.01	20.9	12	12.57	11.05
3-step	MSE (m/s)	9.0442	6.9167	7.7342	3.7011	4.254	3.2441	5-step	12.4765	9.1089	10.1619	6.6403	7.6275	5.6975
	MAE (m/s)	2.4758	2.069	2.2768	1.4621	1.5986	1.3514		2.9377	2.3763	2.613	1.9783	2.1813	1.8934
	MAPE (%)	24.77	21.93	23.21	15.41	16.77	13.9		30.67	25.29	26.97	21.39	23.78	19.61
Summer
1-step	MSE (m/s)	0.3986	0.2957	0.2727	0.2522	0.2437	0.2103	2-step	0.4336	0.3453	0.3165	0.3076	0.3052	0.24
	MAE (m/s)	0.5323	0.453	0.4444	0.3861	0.3732	0.3495		0.5385	0.4741	0.4624	0.426	0.424	0.3665
	MAPE (%)	15.19	13.55	13.48	11.67	11.34	10.63		15.31	14.32	14.24	12.81	12.89	11.11
3-step	MSE (m/s)	0.4829	0.4236	0.3905	0.3509	0.3731	0.2917	5-step	0.5605	0.5792	0.5214	0.3982	0.4984	0.4136
	MAE (m/s)	0.5713	0.5104	0.5026	0.4644	0.4754	0.4148		0.6208	0.6001	0.5815	0.5018	0.5576	0.5049
	MAPE (%)	16.8	16	16.11	14.23	14.87	12.9		18.5	19.34	19.28	15.74	18.08	16.34
Fall
1-step	MSE (m/s)	0.7161	0.54	0.5012	0.4865	0.4872	0.4901	2-step	0.8772	0.7482	0.6455	0.586	0.5816	0.5957
	MAE (m/s)	0.7168	0.5844	0.5675	0.5727	0.5731	0.5733		0.7821	0.7098	0.6587	0.6175	0.6137	0.621
	MAPE (%)	15.59	12.24	11.82	11.79	11.82	11.82		16.94	14.88	13.75	12.77	12.72	12.85
3-step	MSE (m/s)	0.9588	0.8908	0.7079	0.6657	0.6553	0.68	5-step	0.8706	1.1014	0.7552	0.752	0.7259	0.7747
	MAE (m/s)	0.8032	0.7729	0.6902	0.6707	0.6666	0.676		0.7562	0.8413	0.7071	0.703	0.6959	0.7108
	MAPE (%)	17.46	16.3	14.46	13.91	13.86	14.03		16.41	18.06	15.04	14.51	14.43	14.7
Winter
1-step	MSE (m/s)	1.6137	0.6872	0.6367	0.5746	0.5758	0.5683	2-step	2.079	0.7809	0.7208	0.6903	0.6766	0.678
	MAE (m/s)	1.0548	0.6464	0.6414	0.641	0.6314	0.6306		1.1227	0.7051	0.7027	0.7059	0.6933	0.6993
	MAPE (%)	21.17	12.57	12.5	12.31	12.03	12.02		23.1	14.09	13.95	13.77	13.45	13.55
3-step	MSE (m/s)	2.4407	0.8516	0.781	0.7784	0.7552	0.7616	5-step	3.1868	0.9485	0.869	0.821	0.8172	0.816
	MAE (m/s)	1.204	0.74	0.7345	0.7416	0.718	0.7279		1.3773	0.774	0.7643	0.7534	0.7495	0.7516
	MAPE (%)	24.88	15.01	14.71	14.52	13.99	14.15		27.5	15.91	15.38	14.73	14.49	14.5