Metrics mNSE and mIA are monotonically and functionally related, but the use of 2SAD balances the number of deviations evaluated within the numerator and within the denominator of the factional part.
The prediction performance is evaluated with the efficiency metrics nRMSE, mNSE, and mIA, which are presented in Tables 2, 3, and 4 for I-G1, I-G2, and I-G3, respectively.
The mean gain for 1 to 13 weeks of MSVD + MIMO-AR over SWT + MIMO-AR is 17.7% in mNSE and 8.1% in mIA.
Metrics computation gives nRMSE of 2.9%, mNSE of 83.3%, and mIA of 91.6%.
The I-G2 Prediction via MSVD + MIMO-AR for 14 weeks' ahead prediction is shown in Figures 14(a) and 14(b); from figures good fit is observed with nRMSE of 5.8%, mNSE of 81.9%, and mlA of 90.9%.
The highest gain in average MNSE from 1- to 14-step ahead prediction is 7.6%, while average MAPE is 93.3%.
From these figures and metrics, a good fit is observed; the highest accuracy was reached via SSA-AR with MNSE of 87.6%, R2 of 98.6%, MAPE of 2.0%, and RMSE of 1.1%.
The models were evaluated for 14-week ahead forecasting; comparative analysis shows that the proposed models SSA-AR and SSA-ANN achieved the highest accuracy with an average MNSE of 92.6% and 90.3%, respectively; the highest gain in average MNSE achieved by SSA-AR is 7.6%.