# Bitcoin Price Model

I have no idea what I'm doing

**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 | 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: ```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).