1 — Overview
Full summary table
| model | rmse_mean | rmse_std | mae_mean | mae_std | n_folds |
|---|---|---|---|---|---|
| LSTM-GSTARX(24;1) | 71.10 | 6.55 | 54.03 | 3.73 | 5 |
| LSTM-GSTARX(18;1) | 71.20 | 6.69 | 54.08 | 3.90 | 5 |
| LSTM-GSTARX(12;1) | 71.37 | 6.82 | 54.34 | 3.90 | 5 |
| LSTM-GSTARX(6;1) | 72.33 | 7.18 | 54.82 | 4.38 | 5 |
| CASA LSTM-GSTARX(1;1) | 80.34 | 7.62 | 60.63 | 4.11 | 5 |
| LSTM-static (1;1) | 80.36 | 7.64 | 60.64 | 4.13 | 5 |
| GSTARX(1;1) | 88.23 | 4.27 | 68.08 | 2.63 | 5 |
| GSTAR(1;1) | 88.79 | 4.21 | 68.37 | 2.18 | 5 |
2 — Per-Province Rainfall Forecast
Type to search (province name or ISO code), then pick from the box below. Black line = observed rainfall; dashed orange line = model forecast (CASA, LSTM-GSTARX) over the walk-forward test period. The RMSE in the title is the root-mean-square error over all displayed test months (the five walk-forward folds concatenated into one series) for that province — not the average of per-fold RMSEs.
3 — Model Comparison
4 — Diebold-Mariano Test (HLN-corrected)
|−log₁₀(p)| > 1.30 ≈ p < 0.05; > 2.0 ≈ p < 0.01; > 3.0 ≈ p < 0.001. Negative-signed (blue) cells: row outperforms column.
Significant pairs (p < 0.05)
| model_A | model_B | dm_hln | p_value | A_better | sig_001 |
|---|---|---|---|---|---|
| LSTM-GSTARX(6;1) | GSTAR(1;1) | -6.924 | 4.46e-10 | True | True |
| LSTM-GSTARX(24;1) | GSTAR(1;1) | -6.800 | 7.99e-10 | True | True |
| LSTM-GSTARX(18;1) | GSTAR(1;1) | -6.779 | 8.83e-10 | True | True |
| LSTM-GSTARX(12;1) | GSTAR(1;1) | -6.688 | 1.36e-09 | True | True |
| LSTM-GSTARX(6;1) | GSTARX(1;1) | -6.674 | 1.45e-09 | True | True |
| LSTM-GSTARX(24;1) | GSTARX(1;1) | -6.580 | 2.26e-09 | True | True |
| LSTM-GSTARX(18;1) | GSTARX(1;1) | -6.565 | 2.41e-09 | True | True |
| LSTM-GSTARX(12;1) | GSTARX(1;1) | -6.456 | 4.02e-09 | True | True |
| CASA LSTM-GSTARX(1;1) | GSTAR(1;1) | -5.312 | 6.69e-07 | True | True |
| GSTAR(1;1) | LSTM-static (1;1) | 5.288 | 7.41e-07 | False | True |
| LSTM-GSTARX(6;1) | LSTM-static (1;1) | -5.256 | 8.50e-07 | True | True |
| CASA LSTM-GSTARX(1;1) | LSTM-GSTARX(6;1) | 5.238 | 9.17e-07 | False | True |
| LSTM-GSTARX(24;1) | LSTM-static (1;1) | -5.017 | 2.31e-06 | True | True |
| LSTM-GSTARX(18;1) | LSTM-static (1;1) | -5.011 | 2.37e-06 | True | True |
| CASA LSTM-GSTARX(1;1) | LSTM-GSTARX(24;1) | 5.004 | 2.44e-06 | False | True |
| CASA LSTM-GSTARX(1;1) | LSTM-GSTARX(18;1) | 4.997 | 2.51e-06 | False | True |
| LSTM-GSTARX(12;1) | LSTM-static (1;1) | -4.921 | 3.44e-06 | True | True |
| CASA LSTM-GSTARX(1;1) | LSTM-GSTARX(12;1) | 4.907 | 3.64e-06 | False | True |
| CASA LSTM-GSTARX(1;1) | GSTARX(1;1) | -4.670 | 9.50e-06 | True | True |
| GSTARX(1;1) | LSTM-static (1;1) | 4.646 | 1.05e-05 | False | True |
5 — Regime-Stratified RMSE
CASA leans on learned spatial structure during El Niño / La Niña, while the geographic prior dominates in neutral periods (gate α tracks the signed Niño 3.4 index).
6 — α_t Timeline (CASA blending gate)
The CASA blending gate α_t over the test period (left axis) against the Niño 3.4 index (right axis). Lower α_t means more learned spatial structure relative to the geographic prior.
7 — Geographic Network & Per-province RMSE
KNN edges (k=5) overlaid. Marker colour = per-province RMSE from best CASA ablation; orange squares = boundary nodes (PNG, Borneo non-IDN), not forecast targets.