Table 2.
Prediction errors obtained with the univariate model.
| Hours | LSTM | GRU | EMD–LSTM | EMD–GRU | CEEM-LSTM | CEEMD–GRU | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Ahead | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE |
| 1 | 69.42 | 3.49 | 69.53 | 3.60 | 106.85 | 6.27 | 112.66 | 6.89 | 104.76 | 6.27 | 94.02 | 5.67 |
| 2 | 97.24 | 4.82 | 93.91 | 4.73 | 111.63 | 6.14 | 119.68 | 6.98 | 110.52 | 6.33 | 97.11 | 5.48 |
| 3 | 119.56 | 5.80 | 116.50 | 5.64 | 125.51 | 6.66 | 128.12 | 7.15 | 122.53 | 6.86 | 109.98 | 6.01 |
| 4 | 137.90 | 6.61 | 135.58 | 6.38 | 135.31 | 6.92 | 137.77 | 7.42 | 130.80 | 7.19 | 121.18 | 6.41 |
| 5 | 154.67 | 7.31 | 153.48 | 7.18 | 144.56 | 7.25 | 145.52 | 7.61 | 140.77 | 7.66 | 128.60 | 6.58 |
| 6 | 167.24 | 7.91 | 166.15 | 7.70 | 151.24 | 7.49 | 151.45 | 7.72 | 148.90 | 8.08 | 140.58 | 7.16 |
| 7 | 175.19 | 8.38 | 173.31 | 8.01 | 152.77 | 7.54 | 155.85 | 7.89 | 154.80 | 8.40 | 146.93 | 7.48 |
| 8 | 178.11 | 8.66 | 176.53 | 8.32 | 151.75 | 7.41 | 158.87 | 8.06 | 158.51 | 8.62 | 150.03 | 7.57 |
| 9 | 178.63 | 8.80 | 176.53 | 8.48 | 152.70 | 7.52 | 160.49 | 8.23 | 164.65 | 9.00 | 153.98 | 7.76 |
| 10 | 178.71 | 8.95 | 176.52 | 8.67 | 154.56 | 7.60 | 160.38 | 8.25 | 169.22 | 9.29 | 156.35 | 7.78 |
| 11 | 179.73 | 9.17 | 177.44 | 8.95 | 156.97 | 7.64 | 162.72 | 8.33 | 173.60 | 9.55 | 159.01 | 7.80 |
| 12 | 179.50 | 9.35 | 177.43 | 9.20 | 161.12 | 7.70 | 168.04 | 8.55 | 176.56 | 9.61 | 161.69 | 7.81 |
| 13 | 180.23 | 9.49 | 178.59 | 9.38 | 168.32 | 7.93 | 173.91 | 8.73 | 181.56 | 9.81 | 168.17 | 8.15 |
| 14 | 179.63 | 9.49 | 178.81 | 9.47 | 174.55 | 8.10 | 179.56 | 8.93 | 184.19 | 9.84 | 171.19 | 8.27 |
| 15 | 176.61 | 9.36 | 177.02 | 9.44 | 180.36 | 8.21 | 186.42 | 9.18 | 188.09 | 9.89 | 173.41 | 8.29 |
| 16 | 173.04 | 9.11 | 175.40 | 9.31 | 185.50 | 8.39 | 193.16 | 9.40 | 191.02 | 9.87 | 180.15 | 8.54 |
| 17 | 169.15 | 8.91 | 174.58 | 9.17 | 187.40 | 8.51 | 199.68 | 9.67 | 193.14 | 9.82 | 181.39 | 8.55 |
| 18 | 165.71 | 8.69 | 173.18 | 8.99 | 188.03 | 8.54 | 204.25 | 9.89 | 194.14 | 9.70 | 184.97 | 8.62 |
| 19 | 161.09 | 8.36 | 166.95 | 8.62 | 190.05 | 8.63 | 206.01 | 9.91 | 194.83 | 9.65 | 186.10 | 8.51 |
| 20 | 155.07 | 8.01 | 157.97 | 8.14 | 190.60 | 8.59 | 208.22 | 10.00 | 195.12 | 9.65 | 187.34 | 8.54 |
| 21 | 147.68 | 7.56 | 148.73 | 7.65 | 195.03 | 8.72 | 208.29 | 9.93 | 196.03 | 9.71 | 186.85 | 8.52 |
| 22 | 140.75 | 7.19 | 142.09 | 7.32 | 194.34 | 8.60 | 208.17 | 9.87 | 196.82 | 9.77 | 185.40 | 8.40 |
| 23 | 138.15 | 7.03 | 139.43 | 7.12 | 193.49 | 8.43 | 207.63 | 9.77 | 198.40 | 9.88 | 181.90 | 8.23 |
| 24 | 140.45 | 7.22 | 141.06 | 7.18 | 193.51 | 8.36 | 205.86 | 9.64 | 198.82 | 9.96 | 180.76 | 8.25 |
| Mean | 155.98 | 7.90 | 156.11 | 7.86 | 164.42 | 7.80 | 172.61 | 8.67 | 169.49 | 8.93 | 157.80 | 7.68 |
| Std | 28.55 | 1.53 | 28.94 | 1.54 | 26.70 | 0.76 | 30.44 | 1.05 | 29.36 | 1.22 | 29.08 | 0.97 |