# Bitcoin Price Model
**Don't take this seriously. It's all in good fun.**
## The 2024 edition
In November 2024 I asked Claude (3.6 Sonnet, via copy and paste in Claude Web)
to help build a Bitcoin price model. After a lot of branching it produced ~2000
lines of cycle analysis, "market fundamentals", era adjustments and Monte Carlo,
and forecasts like this one (as of 2024-11-14):
In September 2026 a newer Claude scored the forecasts it made on 2024-11-27
against what actually happened:
| | 2024 forecast (median) | Actual |
|---|---|---|
| Cycle top | 2025-10-21, $199K | 2025-10-06, $124.7K |
| 2026-06-30 | $133K (95% floor $65K) | $58.5K |
| 2026-09-23 | $124K | $84.4K |
It called the timing of the top within 15 days, 19 months ahead, but put the
level ~60% too high. "The price stays at $92.7K" was a better forecast (18%
mean error against 68%). Its "95%" intervals were really ~81% intervals past a
year out, thanks to a fudge factor that narrowed them at long horizons.
That code lives in the jj/git history. This is the rewrite.
## How it works now
A forecast is a probability distribution of the price at each horizon, not a
line. Every model produces quantiles of log price, and every model is scored
the same way:
- **Walk-forward.** Every 30 days from 2014 on, each model sees only the data up
to that day and forecasts 1 month to 4 years ahead.
- **CRPS.** Each forecast is scored against what happened with the continuous
ranked probability score, in log-price units (0.1 ≈ "typically 10% off"). It
rewards being sharp and being calibrated at once, and can't be gamed by
narrowing or widening intervals.
- **Baselines.** Skill is reported relative to a zero-drift random walk, with a
90% block-bootstrap interval. Nearby forecasts overlap heavily, so the report
also shows `windows`: the number of genuinely independent outcomes.
- **Holdout.** Development only sees data up to 2024-11-26, the last day the
2024 model saw. Everything after it is held out, and is scored only by
`just holdout`, once per round of model changes. (Caveat: we already know
roughly what happened in 2025-26, so it isn't perfectly blind.)
### Models
- `random_walk`: zero drift; "it stays about here, give or take".
- `drift_rw`: drift equal to the last four years' average; "it keeps doing what
it did last cycle".
- `cycle`: the 2024 model's one real idea. Expected return depends on the day of
the halving cycle, estimated from past cycles, with recent cycles weighted
more.
- `powerlaw`: log price grows linearly in log time since genesis, so growth
keeps slowing. Fitted walk-forward; the exponent has stayed between 5.4 and
6.0 in every fit since 2014.
### Findings so far (development data)
- `cycle` loses to the random walk at every horizon, and so does every setting
tried (recency half-life 0.25-2 cycles, smoothing bandwidth 15-60 days).
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 |
|---|---|---|---|---|---|---|---|
| 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.
### Forward test (from 2026-09-23)
New data is the only honest test left, so forecasts are now recorded before
their outcomes exist. `just snapshot` writes every tracked model's forecast
from the latest price to `data/forecasts/.csv`. It refuses if the price
data is more than two days old or the date already has a snapshot, and the
files are committed so version control dates them. `just forward` scores
every recorded forecast whose target date has passed, the same way the
backtest does.
Tracked: the four registered models plus `powerlaw_ou`, `powerlaw_ou_param`
and `cycle_on_powerlaw`, which development data couldn't settle. Snapshots
store the forecasts themselves, so if a model's definition changes it gets a
new name. The routine is `just weekly` (update, snapshot, score), then commit
the new snapshot. The first 1-month outcomes arrive 2026-10-23; 1-year results
need until late 2027, and 4-year ones until 2030.
## Usage
With Nix:
```sh
nix develop
just update # fetch new daily prices from Coinbase
just backtest # score models on development data -> output/backtest/
just forecast # forecast from the latest price -> output/forecast/
just ab # run A/B experiments -> output/ab/
just weekly # new prices, a forward-test snapshot, and its scores so far
just test
just holdout # score on held-out outcomes; sparingly
```
Without Nix, any Python 3.13 with numpy, pandas 3, scipy and matplotlib works:
`python -m btcmodel --help`.
## Layout
```
btcmodel/
data.py price loading (Investing.com archive + Coinbase), dev cutoff
halving.py halving calendar, position in cycle
forecast.py Forecast (quantiles of log price), CRPS, PIT
evaluate.py walk-forward backtest and summary
experiments.py A/B tests: hypothesis, control, variants, verdict rule
forward.py forward test: record forecasts, score them as outcomes arrive
models/ drift, volatility and shape components; register models in __init__.py
plots.py fan chart, skill and calibration charts
```
A model is any object with a `name` and
`forecast(history, horizons) -> Forecast`. `history` is a date-indexed frame
holding everything up to the forecast origin and nothing after it. Other data
sources (hash rate, on-chain metrics, macro series) can join it as extra
columns. Anything published with a lag must be shifted to the date it was
actually available, or the backtest will quietly cheat.
Price data: [Investing.com](https://www.investing.com/crypto/bitcoin/historical-data)
through 2024-11-26, then Coinbase Exchange daily closes (UTC).