Table 3.
Average MASE for phase 2 forecast selection in the validation sample (2017Q3 to 2019Q4) across all countries.
| Forecast | Base forecasts |
Hierarchical forecasts |
||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| t + 1 | t + 2 | t + 3 | t + 4 | Overall | t + 1 | t + 2 | t + 3 | t + 4 | Overall | |
| Univariate | ||||||||||
| Naive | 4.467 | 5.261 | 4.585 | 1.292 | 3.901 | 4.467 | 5.261 | 4.594 | 1.293 | 3.904 |
| SNaive | 1.589 | 1.589 | 1.637 | 1.292 | 1.527 | 1.590 | 1.590 | 1.638 | 1.293 | 1.528 |
| ETS | 1.348 | 1.479 | 1.600 | 1.329 | 1.439 | 1.350 | 1.485 | 1.596 | 1.323 | 1.439 |
| Theta | 1.309 | 1.463 | 1.622 | 1.415 | 1.452 | 1.304 | 1.461 | 1.623 | 1.410 | 1.450 |
| ARIMA | 1.296 | 1.465 | 1.650 | 1.399 | 1.453 | 1.291 | 1.461 | 1.647 | 1.401 | 1.450 |
| MLP | 1.498 | 1.810 | 2.031 | 1.832 | 1.793 | 1.540 | 1.833 | 2.072 | 1.863 | 1.827 |
| ELM | 1.409 | 1.640 | 1.800 | 1.562 | 1.603 | 1.402 | 1.635 | 1.791 | 1.544 | 1.593 |
| RF | 1.402 | 1.667 | 1.862 | 1.638 | 1.642 | 1.396 | 1.664 | 1.858 | 1.631 | 1.637 |
| THieF-ETS | 1.324 | 1.458 | 1.578 | 1.360 | 1.430 | 1.313 | 1.455 | 1.565 | 1.347 | 1.420 |
| THieF-Theta | 1.328 | 1.495 | 1.669 | 1.450 | 1.486 | 1.325 | 1.491 | 1.669 | 1.446 | 1.483 |
| THieF-ARIMA | 1.291 | 1.441 | 1.625 | 1.366 | 1.431 | 1.283 | 1.436 | 1.614 | 1.372 | 1.426 |
| Multivariate | ||||||||||
| ETSx | 1.378 | 1.550 | 1.691 | 1.391 | 1.503 | 1.379 | 1.544 | 1.685 | 1.373 | 1.495 |
| regARIMA | 1.463 | 1.741 | 2.122 | 1.865 | 1.798 | 1.441 | 1.725 | 2.116 | 1.856 | 1.785 |
| THieF-ETSx | 1.413 | 1.548 | 1.735 | 1.472 | 1.542 | 1.405 | 1.539 | 1.732 | 1.477 | 1.538 |
| THieF-ETSxu | 1.379 | 1.502 | 1.666 | 1.401 | 1.487 | 1.366 | 1.492 | 1.655 | 1.400 | 1.478 |
| THieF-regARIMA | 2.027 | 2.125 | 2.307 | 2.035 | 2.124 | 1.968 | 2.046 | 2.198 | 1.907 | 2.030 |
| THieF-regARIMAu | 1.445 | 1.659 | 1.943 | 1.675 | 1.681 | 1.468 | 1.659 | 1.937 | 1.673 | 1.684 |