The level is the problem: each cycle has grown less than the last (log
return 4.0, 2.6, 2.0, i.e. roughly ×55, ×13, ×7), so any average of past
cycles overshoots.
-`powerlaw` models exactly that, and it is the first model to beat the random
walk with some confidence: +53% and +63% skill at 3 and 4 years, with
unbiased outcomes (mean PIT 0.51). Only 3-4 independent windows back that
up, the functional form is famous *because* it fits Bitcoin's history, and
the holdout hasn't been run yet.
- Its intervals are too wide at long horizons (the 80% interval held every
3-year outcome), because it treats deviations from the trend as permanent.
### A/B tests of the 2024 ideas
`just ab` runs the experiments in `btcmodel/experiments.py`: ideas salvaged
from the old branches (catalogued in [docs/2024-ideas.md](docs/2024-ideas.md)),
each a control plus variants that change one component. Hypotheses and the
verdict rule were written down before anything ran. With ~100 comparisons,
expect a few flukes either way.
| Experiment | Idea | Verdict |
|---|---|---|
| shrink-cycle | scale the cycle drift by 0.25/0.5/0.75 | better, all three: it fixes the level crudely |
| diminishing-returns | power-law trend, optionally reverting to it, or the cycle shape rescaled to it | better (both power-law variants); cycle shape on the power law inconclusive |
| vol-window | EWMA blends, shorter or longer windows | worse: the plain 365-day window wins |
| vol-reversion | volatility reverting to a long-run level or falling trend | worse |
| cycle-vol | volatility by cycle position | inconclusive (no effect) |
| 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 |
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 |
