Table 4.
Average MASE for phase 1 test period (2019Q1 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 | 4.105 | 4.831 | 4.548 | 1.272 | 3.689 | 4.105 | 4.831 | 4.548 | 1.272 | 3.689 |
| SNaive | 1.179 | 1.243 | 1.286 | 1.272 | 1.245 | 1.179 | 1.243 | 1.286 | 1.272 | 1.245 |
| ETS | 1.012 | 1.131 | 1.268 | 1.352 | 1.191 | 1.013 | 1.127 | 1.260 | 1.336 | 1.184 |
| Theta | 0.978 | 1.164 | 1.297 | 1.417 | 1.214 | 0.974 | 1.159 | 1.301 | 1.420 | 1.214 |
| ARIMA | 0.976 | 1.141 | 1.325 | 1.318 | 1.190 | 0.969 | 1.135 | 1.324 | 1.345 | 1.193 |
| MLP | 1.215 | 1.548 | 1.740 | 1.790 | 1.573 | 1.236 | 1.528 | 1.749 | 1.844 | 1.589 |
| ELM | 1.085 | 1.261 | 1.428 | 1.397 | 1.293 | 1.080 | 1.250 | 1.432 | 1.400 | 1.291 |
| RF | 1.116 | 1.324 | 1.526 | 1.533 | 1.375 | 1.117 | 1.325 | 1.529 | 1.537 | 1.377 |
| THieF-ETS | 0.968 | 1.125 | 1.260 | 1.411 | 1.191 | 0.965 | 1.119 | 1.238 | 1.369 | 1.173 |
| THieF-Theta | 0.993 | 1.208 | 1.345 | 1.482 | 1.257 | 0.996 | 1.202 | 1.347 | 1.488 | 1.258 |
| THieF-ARIMA | 0.955 | 1.114 | 1.276 | 1.279 | 1.156 | 0.955 | 1.110 | 1.269 | 1.311 | 1.161 |
| Multivariate | ||||||||||
| ETSx | 1.064 | 1.274 | 1.454 | 1.398 | 1.298 | 1.062 | 1.261 | 1.441 | 1.382 | 1.287 |
| regARIMA | 1.053 | 1.216 | 1.378 | 1.377 | 1.256 | 1.026 | 1.171 | 1.328 | 1.334 | 1.215 |
| THieF-ETSx | 1.097 | 1.291 | 1.539 | 1.509 | 1.359 | 1.092 | 1.273 | 1.526 | 1.490 | 1.345 |
| THieF-ETSxu | 1.046 | 1.259 | 1.472 | 1.480 | 1.314 | 1.035 | 1.235 | 1.448 | 1.438 | 1.289 |
| THieF-regARIMA | 1.828 | 1.914 | 1.862 | 1.840 | 1.861 | 1.762 | 1.825 | 1.724 | 1.655 | 1.742 |
| THieF-regARIMAu | 1.083 | 1.226 | 1.304 | 1.334 | 1.237 | 1.059 | 1.188 | 1.286 | 1.332 | 1.216 |