sam
b0243adf61
Models are now a Composite of drift, volatility and (optional) shape components, so an experiment can swap one part against a fixed control. btcmodel/experiments.py holds seven experiments built from the ideas in the old branches (catalogued in docs/2024-ideas.md), each with its hypothesis and source, and a verdict rule fixed before anything ran. `just ab` runs them on development data. Results: - Shrinking the cycle drift, and a power-law trend (plain or reverting), beat their controls. The power law beats the random walk by 53-63% at 3-4 years with unbiased outcomes, so it is promoted to MODELS. - Every alternative volatility estimate (EWMA blends, other windows, reversion to a level or trend) is worse than the trailing 365-day window. Cycle-dependent volatility, heavy tails and stretched cycle phase show no reliable effect.
141 lines
6.4 KiB
Markdown
141 lines
6.4 KiB
Markdown
# Bitcoin Price Model
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<p align="center">
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<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" />
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</p>
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**Don't take this seriously. It's all in good fun.**
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## The 2024 edition
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In November 2024 I asked Claude (3.6 Sonnet, via copy and paste in Claude Web)
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to help build a Bitcoin price model. After a lot of branching it produced ~2000
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lines of cycle analysis, "market fundamentals", era adjustments and Monte Carlo,
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and forecasts like this one (as of 2024-11-14):
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In September 2026 a newer Claude scored the forecasts it made on 2024-11-27
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against what actually happened:
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| | 2024 forecast (median) | Actual |
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|---|---|---|
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| Cycle top | 2025-10-21, $199K | 2025-10-06, $124.7K |
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| 2026-06-30 | $133K (95% floor $65K) | $58.5K |
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| 2026-09-23 | $124K | $84.4K |
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It called the timing of the top within 15 days, 19 months ahead, but put the
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level ~60% too high. "The price stays at $92.7K" was a better forecast (18%
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mean error against 68%). Its "95%" intervals were really ~81% intervals past a
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year out, thanks to a fudge factor that narrowed them at long horizons.
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That code lives in the jj/git history. This is the rewrite.
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## How it works now
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A forecast is a probability distribution of the price at each horizon, not a
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line. Every model produces quantiles of log price, and every model is scored
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the same way:
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- **Walk-forward.** Every 30 days from 2014 on, each model sees only the data up
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to that day and forecasts 1 month to 4 years ahead.
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- **CRPS.** Each forecast is scored against what happened with the continuous
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ranked probability score, in log-price units (0.1 ≈ "typically 10% off"). It
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rewards being sharp and being calibrated at once, and can't be gamed by
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narrowing or widening intervals.
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- **Baselines.** Skill is reported relative to a zero-drift random walk, with a
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90% block-bootstrap interval. Nearby forecasts overlap heavily, so the report
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also shows `windows`: the number of genuinely independent outcomes.
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- **Holdout.** Development only sees data up to 2024-11-26, the last day the
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2024 model saw. Everything after it is held out, and is scored only by
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`just holdout`, once per round of model changes. (Caveat: we already know
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roughly what happened in 2025-26, so it isn't perfectly blind.)
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### Models
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- `random_walk`: zero drift; "it stays about here, give or take".
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- `drift_rw`: drift equal to the last four years' average; "it keeps doing what
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it did last cycle".
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- `cycle`: the 2024 model's one real idea. Expected return depends on the day of
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the halving cycle, estimated from past cycles, with recent cycles weighted
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more.
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- `powerlaw`: log price grows linearly in log time since genesis, so growth
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keeps slowing. Fitted walk-forward; the exponent has stayed between 5.4 and
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6.0 in every fit since 2014.
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### Findings so far (development data)
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- `cycle` loses to the random walk at every horizon, and so does every setting
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tried (recency half-life 0.25-2 cycles, smoothing bandwidth 15-60 days).
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The level is the problem: each cycle has grown less than the last (log
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return 4.0, 2.6, 2.0, i.e. roughly ×55, ×13, ×7), so any average of past
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cycles overshoots.
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- `powerlaw` models exactly that, and it is the first model to beat the random
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walk with some confidence: +53% and +63% skill at 3 and 4 years, with
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unbiased outcomes (mean PIT 0.51). Only 3-4 independent windows back that
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up, the functional form is famous *because* it fits Bitcoin's history, and
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the holdout hasn't been run yet.
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- Its intervals are too wide at long horizons (the 80% interval held every
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3-year outcome), because it treats deviations from the trend as permanent.
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### A/B tests of the 2024 ideas
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`just ab` runs the experiments in `btcmodel/experiments.py`: ideas salvaged
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from the old branches (catalogued in [docs/2024-ideas.md](docs/2024-ideas.md)),
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each a control plus variants that change one component. Hypotheses and the
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verdict rule were written down before anything ran. With ~100 comparisons,
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expect a few flukes either way.
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| Experiment | Idea | Verdict |
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|---|---|---|
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| shrink-cycle | scale the cycle drift by 0.25/0.5/0.75 | better, all three: it fixes the level crudely |
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| 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 |
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| vol-window | EWMA blends, shorter or longer windows | worse: the plain 365-day window wins |
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| vol-reversion | volatility reverting to a long-run level or falling trend | worse |
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| cycle-vol | volatility by cycle position | inconclusive (no effect) |
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| tails | Student-t, or empirical horizon-level shape | Student-t worse; empirical +5% at 1 month only |
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| cycle-phase | align cycles by fraction elapsed, not days | inconclusive |
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Next: a power law whose deviations revert with bounded variance, and a
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registered test of whether the cycle's timing adds anything on top of it.
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## Usage
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With Nix:
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```sh
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nix develop
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just update # fetch new daily prices from Coinbase
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just backtest # score models on development data -> output/backtest/
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just forecast # forecast from the latest price -> output/forecast/
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just ab # run A/B experiments -> output/ab/
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just test
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just holdout # score on held-out outcomes; sparingly
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```
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Without Nix, any Python 3.13 with numpy, pandas 3, scipy and matplotlib works:
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`python -m btcmodel --help`.
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## Layout
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```
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btcmodel/
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data.py price loading (Investing.com archive + Coinbase), dev cutoff
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halving.py halving calendar, position in cycle
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forecast.py Forecast (quantiles of log price), CRPS, PIT
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evaluate.py walk-forward backtest and summary
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experiments.py A/B tests: hypothesis, control, variants, verdict rule
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models/ drift, volatility and shape components; register models in __init__.py
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plots.py fan chart, skill and calibration charts
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```
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A model is any object with a `name` and
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`forecast(history, horizons) -> Forecast`. `history` is a date-indexed frame
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holding everything up to the forecast origin and nothing after it. Other data
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sources (hash rate, on-chain metrics, macro series) can join it as extra
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columns. Anything published with a lag must be shifted to the date it was
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actually available, or the backtest will quietly cheat.
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Price data: [Investing.com](https://www.investing.com/crypto/bitcoin/historical-data)
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through 2024-11-26, then Coinbase Exchange daily closes (UTC).
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