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Round 2: reverting power law and cycle-on-powerlaw tests; one-time holdout run.

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Add TrendReversionVol: deviations from the power-law trend follow a daily
AR(1), so uncertainty levels off, optionally plus trend-parameter
uncertainty with an autocorrelation-adjusted effective sample size.

Two experiments, run under the unchanged verdict rule:
- powerlaw-ou: +21% to +45% vs powerlaw at 2-4 years, but slightly negative
  point estimates at 1 month make it inconclusive.
- cycle-on-powerlaw: inconclusive (+18% at 2 years, negative elsewhere).

The holdout (outcomes after 2024-11-26) was scored once, for the four
candidates fixed beforehand. powerlaw is the best long-horizon forecast
(+45% and +58% vs the random walk at 2 and 3 years); nothing beats the
random walk inside a year; cycle fails badly. Results are in the README.
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sam
2026-09-24 03:06:21 -07:00
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@@ -96,8 +96,32 @@ expect a few flukes either way.
| tails | Student-t, or empirical horizon-level shape | Student-t worse; empirical +5% at 1 month only |
| cycle-phase | align cycles by fraction elapsed, not days | inconclusive |
Next: a power law whose deviations revert with bounded variance, and a
registered test of whether the cycle's timing adds anything on top of it.
Round 2 tested the power law against two refinements (the verdict rule was
unchanged, and the holdout candidates were fixed before it ran):
| Experiment | Idea | Verdict |
|---|---|---|
| powerlaw-ou | deviations from the trend revert, so uncertainty levels off; optionally plus trend-parameter uncertainty | inconclusive: +21% to +45% at 2-4 years (intervals above zero), but -0.3% and -1% at 1 month fail the "never negative" clause. Bands too narrow without parameter uncertainty, too wide with it |
| cycle-on-powerlaw | the cycle's timing, rescaled to the power-law level | inconclusive: +18% at 2 years, slightly negative at short horizons and 4 years |
### Holdout (run once, 2026-09-24)
Scored on outcomes after 2024-11-26 for the four candidates fixed in advance
(`random_walk`, `drift_rw`, `cycle`, `powerlaw`). The holdout is ~22 months
long, so at 2-4 years it is essentially one outcome period seen from several
origins (1.4-1.9 windows), and the bootstrap intervals there mean little.
| Skill vs random walk | 1mo | 3mo | 6mo | 1y | 2y | 3y | 4y |
|---|---|---|---|---|---|---|---|
| drift_rw | -0% | +1% | +5% | +14% | +31% | +53% | -65% |
| cycle | -14% | -8% | -25% | -104% | -46% | -21% | -179% |
| powerlaw | -1% | -7% | -5% | +3% | +45% | +58% | +15% |
Consistent with development: nothing beats the random walk inside a year,
`cycle` fails badly, and `powerlaw` is the best long-horizon forecast, unbiased
at 2-3 years (mean PIT 0.53-0.56) but with intervals too wide (its 80% interval
held every 2- and 3-year outcome). The holdout is now spent for these models;
a new model needs new data to be tested honestly.
## Usage