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

Table 10

Performance evaluations of different models for the forecast of the one-hour 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)	3.8189	4.002	3.9104	1.9404	1.8876	1.8199	2-step	4.7529	4.8088	4.5033	3.1605	3.4326	3.1185
	MAE (m/s)	1.6305	1.5971	1.6031	1.1912	1.1649	1.143		1.8193	1.8023	1.7529	1.3794	1.4516	1.3555
	MAPE (%)	13.55	13.56	13.2	9.85	9.57	9.42		15.63	15.47	14.58	11.76	12.34	11.47
3-step	MSE (m/s)	6.0454	5.5072	5.0829	3.9493	4.4624	3.8992	5-step	7.7094	6.6719	6.2785	5.3395	6.2761	5.2808
	MAE (m/s)	1.9603	1.9117	1.834	1.5277	1.6338	1.5078		2.1847	2.1189	2.0119	1.8245	1.9751	1.8167
	MAPE (%)	16.76	16.19	15.01	12.88	13.68	12.58		18.74	17.77	16.1	15.34	16.22	14.96
Summer
1-step	MSE (m/s)	0.3249	0.3033	0.289	0.1718	0.1866	0.1732	2-step	0.3683	0.3475	0.3368	0.1911	0.2304	0.1739
	MAE (m/s)	0.4131	0.4046	0.3898	0.3252	0.3342	0.3171		0.4592	0.4465	0.4414	0.3442	0.3737	0.3223
	MAPE (%)	12.1	12.24	11.84	9.27	9.48	8.94		13.32	13.48	13.47	10.07	10.73	9.27
3-step	MSE (m/s)	0.3838	0.4068	0.4013	0.2402	0.2944	0.2029	5-step	0.4521	0.5	0.5067	0.3235	0.3757	0.2663
	MAE (m/s)	0.4788	0.4694	0.4731	0.3751	0.419	0.3451		0.5333	0.5196	0.5304	0.4315	0.4705	0.3896
	MAPE (%)	14.15	14.67	14.97	11.31	12.2	10.14		16.13	16.88	17.49	13.54	13.84	11.75
Fall
1-step	MSE (m/s)	1.1401	0.8356	0.8062	0.5619	0.4867	0.5122	2-step	1.5353	1.0856	1.0266	0.9874	0.7936	0.7479
	MAE (m/s)	0.9306	0.7736	0.7577	0.6446	0.593	0.5914		1.0578	0.86	0.8309	0.8106	0.7297	0.6882
	MAPE (%)	20.25	16.2	15.68	12.62	11.71	12		22.74	17.87	17	15.81	14.37	13.91
3-step	MSE (m/s)	1.5995	1.1857	1.1158	1.3834	1.0994	1.0397	5-step	1.5644	1.239	1.1143	1.5687	1.2873	1.3849
	MAE (m/s)	1.062	0.8895	0.857	0.9206	0.834	0.8154		1.0399	0.9121	0.8637	0.9556	0.8883	0.9313
	MAPE (%)	22.9	18.35	17.35	18.04	16.57	16.63		22.64	19.22	17.76	19.01	18.08	19.47
Winter
1-step	MSE (m/s)	0.8207	0.4931	0.5235	0.4726	0.4589	0.4658	2-step	1.35	0.6226	0.6651	0.5605	0.5481	0.5595
	MAE (m/s)	0.7238	0.5613	0.5871	0.4794	0.4757	0.4707		0.9529	0.6408	0.6697	0.5721	0.5701	0.571
	MAPE (%)	11.63	9.17	9.62	8.03	8.01	7.95		15.67	10.43	10.97	9.43	9.47	9.54
3-step	MSE (m/s)	1.9413	0.6929	0.7451	0.6288	0.605	0.6022	5-step	3.4093	0.7917	0.837	0.7601	0.6951	0.6894
	MAE (m/s)	1.1112	0.6877	0.7223	0.6169	0.6143	0.6127		1.4227	0.7494	0.7776	0.6901	0.6777	0.674
	MAPE (%)	18.31	11.25	11.95	10.02	10.13	10.17		23.55	12.22	12.94	10.89	11.05	11.03