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

Table 9

Performance evaluations of different models for the forecast of the one-hour 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)	3.5491	2.6786	2.5691	1.3928	1.3207	1.1857	2-step	4.8962	3.5233	3.3591	2.0892	2.071	2.2118
	MAE (m/s)	1.488	1.2338	1.1719	0.917	0.9008	0.879		1.7826	1.4945	1.4178	1.0479	1.054	1.1309
	MAPE (%)	20.5	17.55	16.54	13.59	13.2	12.54		25.23	21.59	20.23	15.19	15.12	15.95
3-step	MSE (m/s)	4.9024	3.649	3.5204	2.6858	2.8108	3.7149	5-step	5.3601	3.6718	3.616	2.7484	3.1291	5.4178
	MAE (m/s)	1.7797	1.5561	1.4819	1.2117	1.2498	1.4508		1.8963	1.5616	1.5003	1.2732	1.3735	1.7669
	MAPE (%)	24.92	22.22	20.82	17.25	17.65	20.37		26.43	22.03	20.62	17.86	19.1	24.89
Summer
1-step	MSE (m/s)	0.4484	0.3349	0.2988	0.2956	0.2991	0.2871	2-step	0.3988	0.3094	0.2506	0.3168	0.3106	0.2945
	MAE (m/s)	0.5476	0.4808	0.451	0.4385	0.4395	0.4283		0.4988	0.4558	0.4016	0.4547	0.449	0.4317
	MAPE (%)	15.13	14.3	13.1	12.83	12.91	12.62		13.73	13.59	11.52	13.04	12.94	12.48
3-step	MSE (m/s)	0.4349	0.3361	0.245	0.3588	0.343	0.3256	5-step	0.4863	0.4093	0.2582	0.4176	0.3804	0.3691
	MAE (m/s)	0.5286	0.4736	0.3973	0.4899	0.48	0.4567		0.5748	0.5177	0.4189	0.5304	0.5	0.4878
	MAPE (%)	14.57	14.26	11.42	13.96	13.76	13.16		15.91	15.88	12.18	14.91	14.28	14.14
Fall
1-step	MSE (m/s)	0.7452	0.5487	0.4813	0.3457	0.3399	0.3174	2-step	0.9214	0.8502	0.696	0.6654	0.6462	0.6252
	MAE (m/s)	0.7107	0.6559	0.6106	0.4473	0.441	0.4305		0.7608	0.7823	0.7093	0.6265	0.6117	0.6247
	MAPE (%)	12.74	11.19	10.58	7.69	7.62	7.41		13.61	12.95	12.11	10.66	10.48	10.69
3-step	MSE (m/s)	1.0666	1.09	0.8224	0.9081	0.8629	0.8287	5-step	1.086	1.3202	0.8961	1.1529	1.0374	1.0159
	MAE (m/s)	0.8368	0.8473	0.752	0.7382	0.7208	0.7164		0.8329	0.9354	0.7681	0.823	0.7944	0.7929
	MAPE (%)	15.23	13.82	12.73	12.28	12.07	11.97		15.32	15.44	13.21	13.85	13.44	13.38
Winter
1-step	MSE (m/s)	0.8732	0.5293	0.4903	0.4433	0.4465	0.4397	2-step	1.0566	0.6481	0.5735	0.5438	0.5476	0.5512
	MAE (m/s)	0.7766	0.5785	0.5512	0.522	0.5217	0.511		0.8729	0.6463	0.5842	0.5677	0.5645	0.5573
	MAPE (%)	13.09	10.06	9.4	8.98	8.97	8.75		15.03	11.51	10.13	9.78	9.72	9.54
3-step	MSE (m/s)	1.5411	0.8365	0.7038	0.6564	0.6605	0.671	5-step	2.1199	1.0782	0.8526	0.7186	0.7207	0.7353
	MAE (m/s)	1.0077	0.7348	0.6595	0.6252	0.6211	0.6212		1.1633	0.8229	0.7431	0.6621	0.6582	0.6585
	MAPE (%)	17.6	13.32	11.56	10.84	10.75	10.69		20.42	15.11	13.04	11.49	11.39	11.26