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 |
