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

Table 6

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

	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)	1.7933	1.3933	1.3314	0.5031	0.4979	0.486	2-step	2.2254	1.7834	1.6877	0.9475	0.9395	0.9143
	MAE (m/s)	0.9946	0.9531	0.934	0.5744	0.5717	0.5591		1.1299	1.0699	1.0411	0.7536	0.7498	0.7401
	MAPE (%)	16.16	9.62	9.45	5.85	5.82	5.7		17.82	10.8	10.54	7.68	7.64	7.56
3-step	MSE (m/s)	2.8511	2.1217	1.9957	1.3859	1.3794	1.3498	5-step	3.0363	2.5219	2.3401	1.9192	1.9249	1.8929
	MAE (m/s)	1.2173	1.1613	1.1246	0.8957	0.8953	0.8853		1.2432	1.2569	1.2031	1.0468	1.0478	1.0436
	MAPE (%)	19.37	11.77	11.44	9.11	9.09	9.05		19.33	12.57	12.09	10.46	10.46	10.52
Summer
1-step	MSE (m/s)	0.4929	0.4557	0.4809	0.1818	0.1768	0.1642	2-step	0.5592	0.5071	0.5184	0.2389	0.2334	0.2132
	MAE (m/s)	0.5475	0.518	0.5254	0.3436	0.3399	0.3255		0.5966	0.5697	0.5723	0.3872	0.3844	0.3699
	MAPE (%)	8.19	7.72	7.86	5.11	5.07	4.85		8.92	8.41	8.48	5.73	5.69	5.45
3-step	MSE (m/s)	0.6594	0.5928	0.5985	0.3242	0.3167	0.2976	5-step	0.8018	0.7361	0.7424	0.505	0.4903	0.512
	MAE (m/s)	0.6502	0.6166	0.6169	0.4436	0.4393	0.4305		0.7195	0.6859	0.6854	0.5508	0.5428	0.5545
	MAPE (%)	9.73	9.08	9.12	6.57	6.51	6.28		10.76	10.04	10.06	8.21	8.1	8.03
Fall
1-step	MSE (m/s)	0.416	0.4438	0.1106	0.1936	0.19	0.1847	2-step	0.5802	0.6031	0.1103	0.3085	0.3089	0.2995
	MAE (m/s)	0.4926	0.5046	0.2576	0.3432	0.3409	0.3381		0.5703	0.5767	0.257	0.4175	0.4149	0.4099
	MAPE (%)	7.76	7.75	8.68	5.46	5.41	5.39		8.78	8.71	8.71	6.55	6.48	6.44
3-step	MSE (m/s)	0.708	0.7263	0.1281	0.4589	0.4774	0.4601	5-step	0.8672	0.8777	0.1541	0.6675	0.7352	0.7026
	MAE (m/s)	0.6275	0.626	0.279	0.506	0.5037	0.5002		0.7024	0.6854	0.3082	0.6128	0.6181	0.6193
	MAPE (%)	9.56	9.37	9.46	7.85	7.75	7.75		10.61	10.15	1.05	9.35	9.3	9.39
Winter
1-step	MSE (m/s)	0.5337	0.5718	0.6338	0.3426	0.3371	0.3086	2-step	0.8135	0.8456	0.9081	0.5718	0.5991	0.5244
	MAE (m/s)	0.5685	0.5933	0.6283	0.4647	0.4517	0.4376		0.6836	0.7078	0.7279	0.5824	0.592	0.5574
	MAPE (%)	8.23	9.71	10.14	7.47	7.24	7.05		9.85	11.59	11.68	9.26	9.45	8.85
3-step	MSE (m/s)	1.0503	1.0935	1.1473	0.8221	0.8712	0.7726	5-step	1.4387	1.4821	1.5336	1.2745	1.3178	1.2256
	MAE (m/s)	0.7791	0.7882	0.8049	0.6836	0.7038	0.6626		0.9043	0.9081	0.9213	0.835	0.854	0.8228
	MAPE (%)	11.14	12.91	12.87	10.8	11.2	10.45		12.65	14.86	14.65	13.14	13.5	12.92