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

Table 5

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

	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)	1.5112	1.5822	1.3404	0.4362	0.4433	0.4317	2-step	2.1976	2.3299	1.8691	0.9032	0.9068	0.8717
	MAE (m/s)	0.9583	0.9781	0.9151	0.5184	0.5181	0.5183		1.1455	1.182	1.057	0.7154	0.7171	0.7055
	MAPE (%)	7.75	7.89	7.4	4.21	4.2	4.2		9.34	9.55	8.57	5.82	5.81	5.72
3-step	MSE (m/s)	2.7135	3.0059	2.2917	1.4506	1.439	1.3738	5-step	3.1234	3.5938	2.701	2.0879	2.1161	1.9795
	MAE (m/s)	1.2682	1.3242	1.1629	0.8828	0.8827	0.8655		1.3667	1.4767	1.2655	1.0698	1.0719	1.043
	MAPE (%)	10.34	10.68	9.41	7.19	7.15	7.01		11.06	11.85	10.15	8.65	8.6	8.37
Summer
1-step	MSE (m/s)	0.4632	0.6339	0.449	0.1755	0.1665	0.1628	2-step	0.6472	1.0769	0.6471	0.369	0.3525	0.3398
	MAE (m/s)	0.5074	0.602	0.4956	0.31	0.3025	0.3023		0.6055	0.7833	0.6038	0.4504	0.4425	0.4386
	MAPE (%)	6.3	7.09	6.02	3.74	3.67	3.67		7.54	9.11	7.31	5.4	5.34	5.3
3-step	MSE (m/s)	0.8074	1.5554	0.8309	0.5901	0.5753	0.5581	5-step	1.0994	2.4044	1.1971	0.9631	0.9914	0.937
	MAE (m/s)	0.6787	0.9364	0.6858	0.5616	0.5552	0.5497		0.8095	1.1767	0.8246	0.7215	0.725	0.7082
	MAPE (%)	8.5	10.77	8.27	6.7	6.66	6.62		10.17	13.39	9.84	8.54	8.58	8.47
Fall
1-step	MSE (m/s)	0.2504	0.2578	0.2398	0.1271	0.1265	0.1225	2-step	0.3173	0.3319	0.2977	0.1859	0.1886	0.1827
	MAE (m/s)	0.3894	0.3852	0.3773	0.262	0.2606	0.2557		0.4337	0.4349	0.4181	0.3243	0.3258	0.3201
	MAPE (%)	5.18	5.04	4.96	3.43	3.41	3.38		5.69	5.62	5.44	4.20	4.22	4.19
3-step	MSE (m/s)	0.3705	0.3909	0.3449	0.2449	0.2512	0.2444	5-step	0.4391	0.492	0.4141	0.3329	0.3509	0.341
	MAE (m/s)	0.4659	0.4659	0.4487	0.3714	0.3767	0.3721		0.5114	0.5322	0.4981	0.4382	0.4491	0.4491
	MAPE (%)	6.07	5.97	5.8	4.79	4.85	4.85		6.6	6.75	6.39	5.63	5.74	5.83
Winter
1-step	MSE (m/s)	0.5426	0.5362	0.5508	0.3184	0.2908	0.28	2-step	0.8537	0.7711	0.7896	0.5109	0.4902	0.4721
	MAE (m/s)	0.5754	0.5681	0.5735	0.4421	0.4256	0.4171		0.6887	0.6718	0.6755	0.5472	0.5358	0.5273
	MAPE (%)	9.38	8.23	8.27	6.36	6.19	6.03		11.08	9.68	9.64	7.78	7.61	7.52
3-step	MSE (m/s)	1.1557	0.9653	0.9953	0.7207	0.7013	0.6828	5-step	1.6309	1.2887	1.3295	1.072	1.0714	1.038
	MAE (m/s)	0.796	0.7404	0.7509	0.6294	0.6216	0.6127		0.9501	0.8451	0.8573	0.7537	0.752	0.7387
	MAPE (%)	12.67	10.54	10.58	8.87	8.7	8.67		14.83	11.83	11.85	10.42	10.3	10.24