bitcoin-model/README.md

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), 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.

Usage

With Nix:

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 through 2024-11-26, then Coinbase Exchange daily closes (UTC).