# Bitcoin Price Model

<p align="center">
  <img src="https://img.izismile.com/img/img5/20120417/640/i_have_no_idea_what_im_doing_meme_640_07.jpg" alt="I have no idea what I'm doing" />
</p>

**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):

![moooooon](docs/2024-forecast.png)

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 |

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.

## 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 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
  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).