Table 5.
Metric values of the candidate models for different time horizons (T)
| Model | T | MAE | MSE | RMSE |
| GNNq (1) | 1h | 171.923 (± 202.484) | 120,676.856 (± 629,199.550) | 223.957 (± 265.603) |
| GNNd (1) | 215.477 (± 266.398) | 206,847.458 (± 912,681.937) | 287.782 (± 352.239) | |
| GNNgr (1) | 136.877 (± 146.642) | 76,152.625 (± 409,849.719) | 185.753(± 204.116) | |
| GNNqgr (1) | 160.940 (± 171.504) | 102,270.633 (± 479,770.322) | 215.096 (± 236.694) | |
| GNNsl (1) | 164.947 (± 173.624) | 99,771.510 (± 481495.175) | 215.585 (± 230.896) | |
| ARIMA (2844) | 131.613 (± 189.702) | 53,295.374 (± 249,934.954) | 174,313 (± 245.913) | |
| LSTM (2844) | 287.582 (± 249.103) | 240,392.048 (± 673,797.631) | 364.926 (± 327.504) | |
| Naive | 445.657 (± 573.288) | 844,369.636 (± 3,552,303.321) | 564.808 (± 724.946) | |
| GNNq (1) | 3h | 168.832 (± 188.286) | 126,225.899 (± 562,311.371) | 235.882 (± 265.726) |
| GNNd (1) | 164.528 (± 182.431) | 127,471.411 (± 571,985.433) | 236.079 (± 267.887) | |
| GNNgr (1) | 143.100 (± 144.381) | 79,202.233 (± 309,171.505) | 196.715 (± 201.295) | |
| GNNqgr (1) | 149.769 (± 168.372) | 93,474.430 (± 460,505.513) | 202.048 (± 229.498) | |
| GNNsl (1) | 172.606 (± 182.565) | 117,719.663 (± 490,176.192) | 233.887 (± 251.075) | |
| ARIMA (2844) | 229.139 (± 283.488) | 172512.497 (± 839,840.629) | 264.666 (± 320.454) | |
| LSTM (2844) | 268.269 (± 215.494) | 192,273.747 (± 525,928.089) | 338.988 (± 278.197) | |
| Naive | 445.657 (± 573.288) | 844,369.636 (± 3,552,303.321) | 564.808 (± 724.946) | |
| GNNq (1) | 6h | 186.570 (± 208.805) | 157,179.349 (± 657,231.586) | 261.085 (± 298.405) |
| GNNd (1) | 197.032 (± 217.406) | 169,179.710 (± 713,804.705) | 270.959 (± 309.507) | |
| GNNgr (1) | 156.773 (± 163.219) | 95,958.014 (± 389,080.101) | 211.768 (± 226.120) | |
| GNNqgr (1) | 166.788 (± 183.809) | 114,271.417 (± 505,934.955) | 223.819 (± 253.375) | |
| GNNsl (1) | 177.517 (± 190.946) | 139,345.311 (± 589,300.754) | 248.903 (± 278.245) | |
| ARIMA (2844) | 237.026 (± 243.406) | 152,980.337 (± 299,022.317) | 280.883 (± 275.1284) | |
| LSTM (2844) | 290.504 (± 221.231) | 215,440.658 (± 585,540.530) | 362.157 (± 290.377) | |
| Naive | 685.219 (± 915.489) | 1,880,087.023 (± 8,132,191.379) | 827.188 (± 1093.740) | |
| GNNq (1) | 12h | 187.419 (± 229.787) | 189,112.463 (± 913,244.057) | 269.144 (± 341.636) |
| GNNd (1) | 206.836 (± 267.642) | 239,994.215 (± 1,206,237.416) | 295.081 (± 391.120) | |
| GNNgr (1) | 193.796 (± 234.397) | 195,603.403 (± 949,279.271) | 277.460 (± 344.472) | |
| GNNqgr (1) | 159.373 (± 187.872) | 118,149.585 (± 599,204.577) | 218.187 (± 265.648) | |
| GNNsl (1) | 179.012 (± 220.276) | 182,799.867 (± 898,308.893) | 261.680 (± 338.177) | |
| ARIMA (2844) | 216.664 (± 205.569) | 128,209.707 (± 230,840.883) | 263.832 (± 244.696) | |
| LSTM (2844) | 252.473 (± 267.717) | 238,852.906 (± 1,135,378.617) | 330.673 (± 359.992) | |
| Naive | 940.104 (± 1,265.396) | 3,209,833.152 (± 14,297,120.361) | 1,068.467 (± 1,438.381) |
The number in brackets in the Model column indicates the number of instances of each model. The lower values of each metric for the GNN models are shown in bold