IWA Publishing

The single-stage forecast procedure tries four models: SVR, RF, Ridge, and ANN. The first stage of the two-stage forecast procedure uses SVR, and the second stage tries the same four models as in the single-stage version. So, we denote the two-stage models as SVR–SVR, SVR–RF, SVR–Ridge, and SVR–ANN. Tables 5 and 6 show the comparison of the average forecast error of the two-stage forecast procedure with that of the single-stage forecast procedure as h increases from 1 to 8. Figures 8 and 9 present the contents of Tables 4 and 5 in line chart form. In each figure, the horizontal axis is the number of periods h, and the vertical axis is the RMSE or MAE.

Table 5

Comparison of the average forecast error (h = 1, 2, 3, 4)

Model	RMSE (h = 1)	MAE (h = 1)	RMSE (h = 2)	MAE (h = 2)	RMSE (h = 3)	MAE (h = 3)	RMSE (h = 4)	MAE (h = 4)
SVR	0.0266	0.0233	0.0291	0.0252	0.0329	0.0286	0.0369	0.0323
SVR–SVR	0.0149	0.0123	0.0194	0.0169	0.0214	0.0188	0.021	0.0184
RF	0.0934	0.086	0.0871	0.0791	0.0932	0.0855	0.0928	0.0849
SVR–RF	0.0868	0.0789	0.088	0.0799	0.0884	0.0805	0.0865	0.078
Ridge	0.0243	0.0209	0.0236	0.0203	0.0291	0.0248	0.0341	0.0299
SVR–Ridge	0.0162	0.014	0.0177	0.0149	0.0146	0.0125	0.0162	0.0141
ANN	0.0133	0.0109	0.0138	0.0122	0.0164	0.0143	0.0136	0.0116
SVR–ANN	0.0099	0.0087	0.0106	0.0091	0.0124	0.0101	0.0122	0.0103

Model	RMSE (h = 1)	MAE (h = 1)	RMSE (h = 2)	MAE (h = 2)	RMSE (h = 3)	MAE (h = 3)	RMSE (h = 4)	MAE (h = 4)
SVR	0.0266	0.0233	0.0291	0.0252	0.0329	0.0286	0.0369	0.0323
SVR–SVR	0.0149	0.0123	0.0194	0.0169	0.0214	0.0188	0.021	0.0184
RF	0.0934	0.086	0.0871	0.0791	0.0932	0.0855	0.0928	0.0849
SVR–RF	0.0868	0.0789	0.088	0.0799	0.0884	0.0805	0.0865	0.078
Ridge	0.0243	0.0209	0.0236	0.0203	0.0291	0.0248	0.0341	0.0299
SVR–Ridge	0.0162	0.014	0.0177	0.0149	0.0146	0.0125	0.0162	0.0141
ANN	0.0133	0.0109	0.0138	0.0122	0.0164	0.0143	0.0136	0.0116
SVR–ANN	0.0099	0.0087	0.0106	0.0091	0.0124	0.0101	0.0122	0.0103

View Large

Table 6

Comparison of the average forecast error (h = 5, 6, 7, 8)

Model	RMSE (h = 5)	MAE (h = 5)	RMSE (h = 6)	MAE (h = 6)	RMSE (h = 7)	MAE (h = 7)	RMSE (h = 8)	MAE (h = 8)
SVR	0.0414	0.0361	0.0451	0.0391	0.0497	0.0424	0.0522	0.0426
SVR–SVR	0.0282	0.0242	0.0304	0.026	0.0321	0.0271	0.039	0.0352
RF	0.0906	0.0824	0.0888	0.0807	0.0927	0.0833	0.0894	0.0803
SVR–RF	0.0867	0.0781	0.0821	0.0734	0.0813	0.0722	0.0853	0.0762
Ridge	0.036	0.0312	0.0383	0.0325	0.0403	0.0339	0.0428	0.0357
SVR–Ridge	0.017	0.014	0.0189	0.0161	0.0207	0.0171	0.0251	0.0217
ANN	0.016	0.0139	0.0153	0.0131	0.0164	0.0138	0.0173	0.0157
SVR–ANN	0.0154	0.013	0.0148	0.0124	0.0148	0.0128	0.016	0.0137

Model	RMSE (h = 5)	MAE (h = 5)	RMSE (h = 6)	MAE (h = 6)	RMSE (h = 7)	MAE (h = 7)	RMSE (h = 8)	MAE (h = 8)
SVR	0.0414	0.0361	0.0451	0.0391	0.0497	0.0424	0.0522	0.0426
SVR–SVR	0.0282	0.0242	0.0304	0.026	0.0321	0.0271	0.039	0.0352
RF	0.0906	0.0824	0.0888	0.0807	0.0927	0.0833	0.0894	0.0803
SVR–RF	0.0867	0.0781	0.0821	0.0734	0.0813	0.0722	0.0853	0.0762
Ridge	0.036	0.0312	0.0383	0.0325	0.0403	0.0339	0.0428	0.0357
SVR–Ridge	0.017	0.014	0.0189	0.0161	0.0207	0.0171	0.0251	0.0217
ANN	0.016	0.0139	0.0153	0.0131	0.0164	0.0138	0.0173	0.0157
SVR–ANN	0.0154	0.013	0.0148	0.0124	0.0148	0.0128	0.016	0.0137

View Large

Figure 8

View large Download slide

Comparison of RMSE.

Figure 9

View large Download slide

Comparison of MAE.

This Feature Is Available To Subscribers Only