Base grid
8 × 8 × 7 = 448
- tau_B: 0.5…5 y (8)
- tau_R: 5…25 y (8)
- alpha: 0.1…0.7 (7)
Seven declared points have tau_B = tau_R = 5. They remain in the audit grid, but the S1 constraint excludes them from fitting: 441 admissible points.
翻訳が完成するまで、このページの一部は英語で表示されます。
DKC Model Comparison
A pre-specified M0–M4 comparison contract with BIC, country holdout and temporal holdout—without declaring a winner before eligible data exist.
No M0–M4 winner is published. The current national series are technology-timing proxies, the two kernel regressors are highly collinear, and M4 is not identifiable without spectral and endpoint-matched measurements.
1. M0–M4
| Model | Parameters | Description | Current status | BIC |
|---|---|---|---|---|
| M0 | 0 | nullconstant TFR comparator | Comparison contract ready | not scored |
| M1 | 1 | cumulative proxylegacy cumulative technology proxy | Comparison contract ready | not scored |
| M2 | 2 | single exponentialone normalized lag kernel | Comparison contract ready | not scored |
| M3 | 4 | base DKCtwo normalized kernels plus bounded Hill mapping | Comparison contract ready | not scored |
| M4 | 8-10 | refined DKCT1-T12 candidate calculation | NOT_IDENTIFIABLE_WITH_CURRENT_DATA | not scored |
BIC = n_obs × ln(MSE) + k × ln(n_obs)
2. Pre-specified grids
Refined grid
6 × 6 × 5 × 6 × 4 = 4320
- tau_B: 0.3…2 y (6)
- tau_R: 5…20 y (6)
- alpha: 0.2…0.6 (5)
- n: 1.0…3.5 (6)
- n_B: 2…5 (4)
Every point satisfies tau_R > tau_B. Beta is always derived as 1 − alpha.
3. Leakage-free evaluation order
- 1Lock input provenance as PROXY or measured FieldState; never merge the two classes.
- 2Fit each parameter candidate on training countries only.
- 3Hold out one complete country and evaluate it without using its outcomes in fitting.
- 4Repeat for every country and calculate LOOCV error and BIC without a pre-declared winner.
- 5For temporal validation, fit through 2015 and evaluate 2016–2024; the UN WPP 2024 projection is not an observation, so WPP scoring ends in 2023.
- 6Lock a forecast only after external validation and an identifiability test.
Current identifiability result
In the current monotonic technology-timing proxy, the fast and slow regressors correlate above 0.98. The positivity-constrained slow weight collapses to zero, so tau_R and the alpha/(1−alpha) split cannot be locked from this dataset. This is a result, not a missing interface value.