Methodology¶
A short version of the method. The paper in paper/ has the full argument.
Null model¶
Prophet is fitted to ln y. A piecewise-linear trend on the log scale is
piecewise exponential growth: the "boring world". Persistent one-sided
residuals against it are evidence that the world is not boring.
Acceleration: δ and t_c¶
Hyperbolic growth dx/dt = k x^(1+δ) reaches infinity at a finite time t_c.
With g = d ln x / dt,
g is estimated from historical data with a cross-validated smoother, never
from the forecast segment (design note D1). Intervals come from a moving block
bootstrap (D4). LPPLS gives an independent t_c.
Recursion: κ¶
The out-of-sample skill gained by adding capability's own lags to a NeuralProphet model that already has the exogenous drivers. It is reported against a permutation null (D9).
Vinge Horizon: h*¶
The first forecast horizon at which the smoothed rolling-origin error, measured
in log units, crosses a factor tolerance (D2, D3). A shrinking h*(t) means
the world is getting harder to forecast.
Jonas Gap: dG/dt¶
G = ln C − ln H, normalised at a base year. Only its velocity carries meaning
(D8).
Decision rules¶
- Jonas: alarm when
P(danger) > 1/(1+λ).λis published in YAML. - Rawls: report the maximin decision next to the expected-value one.
- Collingridge: report lead time until the upper quantile crosses the threshold.
- Popper: every forecast is pre-registered in a hash-chained ledger.
| Level | Trigger |
|---|---|
| 0 Normal | All dials calm |
| 1 Watch | One dial in danger |
| 2 Warning | Two dials, or one on 3+ independent metrics |
| 3 Alarm | Three dials |
| 4 Kairos | All four dials |