Table 1.
MASEs and standard deviation of MASEs for all models.
| MASE |
Std. Deviation of MASEs |
MASE |
Std. Deviation of MASEs |
||
|---|---|---|---|---|---|
| 11 single models | 26 stacking models | ||||
| SNAIVE | 1.2717 | 1.0761 | Regression | 4.1632 | 23.8915 |
| SARIMA | 1.1172 | 1.0384 | bn3ps | 1.0229 | 0.9313 |
| ETS | 1.0811 | 0.9252 | bn3pe | 1.0206 | 0.9275 |
| STL | 1.1113 | 0.9088 | bn3p2 | 1.0199 | 0.9253 |
| TBATS | 1.3115 | 1.0644 | bn3pc | 1.0211 | 0.9275 |
| ELM | 1.2286 | 1.6337 | bn3rs | 1.0236 | 0.9593 |
| MLP | 1.3285 | 2.1095 | bn3re | 1.0220 | 0.9543 |
| ARDL | 1.4069 | 0.9062 | bn3r2 | 1.0242 | 0.9567 |
| SRTVP | 3.1527 | 2.7749 | bn3rc | 1.0232 | 0.9581 |
| ELMX | 1.2690 | 1.1581 | bn3as | 1.0215 | 0.9224 |
| MLPX | 1.4367 | 1.2125 | bn3ae | 1.0206 | 0.9184 |
| bn3a2 | 1.0206 | 0.9181 | |||
| bn3ac | 1.0211 | 0.9182 | |||
| bn5ps | 1.0047 | 0.9641 | |||
| bn5pe | 1.0009 | 0.9602 | |||
| bn5p2 | 1.0002 | 0.9665 | |||
| bn5pc | 1.0019 | 0.9599 | |||
| bn5rs | 0.9980 | 0.9059 | |||
| bn5re | 0.9969 | 0.9062 | |||
| bn5r2 | 0.9980 | 0.9059 | |||
| bn5rc | 0.9972 | 0.9062 | |||
| bn5as | 1.0062 | 0.9612 | |||
| bn5ae | 1.0040 | 0.9579 | |||
| bn5a2 | 1.0050 | 0.9609 | |||
| bn5ac | 1.0043 | 0.9578 | |||
| sn | 1.0269 | 0.9851 | |||
| Average | 1.4287 | 1.3462 | Average | 1.0122 | 0.9406 |
Note: The first two digits, “bn”, stand for “best n” type of stacking methods, with the third digit representing the number of preliminary single models used in stacking, the fourth digit representing the criteria of selecting the best models (p – MAPE, r – RMSE, a – MASE), and the fifth digit representing the method of combining the selected models (s – simple average, e – error weighting, 2 – squared error weighting, c – selection criteria based weighting).