wasserstein-btc

Distributional forecasting for crypto returns via geodesics on the 2-Wasserstein manifold of probability measures

A small, falsifiable, interpretable distributional forecaster — ~4 hyperparameters, no learned weights, no neural net.

Live dashboard · Theory · Research report · Results · Roadmap

wasserstein-btc forecasts the whole conditional distribution of future log-returns — not the mean and not the variance — for liquid crypto pairs at horizons of 1, 5 and 21 days. The market is modelled as a trajectory on the 2-Wasserstein manifold of probability measures, the forecast is the tangent-space extrapolation of recent quantile vectors, and the result is scored with strictly proper rules (CRPS) against an explicit panel of baselines (Static, RW-Drift, Historical-Simulation Bootstrap, GARCH-N, GARCH-t, GJR-GARCH-t).

What it is: a small, falsifiable, interpretable distributional forecaster — ~4 hyperparameters, no learned weights, no neural net. What it is not: a trading-signal generator, a multivariate risk system, or a benchmark against state-of-the-art realised-volatility models (see docs/RESEARCH_REPORT.md §6 for what is not claimed, and ROADMAP.md for the v0.4 priorities that would close that gap).

Contents

• Headline result · what the panel shows
• Install · uv sync or pip install wbtc
• Quick start — CLI · one-line forecasts and backtests
• Quick start — Python · the forecast() API
• What's novel · the four contributions
• Documents · where to read the theory and the numbers
• Honest limitations · what is not claimed
• Citation · how to cite

Headline result

On the v0.4 panel (BTC + ETH + SOL + BNB × h ∈ {1, 5, 21} × 6.75 years walk-forward; 1380–2470 test days per cell), the WGeo family beats the best non-WGeo baseline (best of Static / RW-Drift / HS-Bootstrap / GARCH-N / GARCH-t / GJR-GARCH-t) in 12 / 12 cells by 0.1% to 3.2% mean CRPS.

The v0.4 cycle adds (a) WGeoEnsemble, the W₂ barycentre of the v0.3 trio in quantile-function coordinates — guaranteed by Jensen's inequality on convex CRPS to weakly dominate the component average; and (b) a residualised Diebold-Mariano test (Giacomini-White 2006) that projects out shared volatility-clustering noise via |y|, y², y plus peer-method losses, preserving the EPA null while strictly reducing HAC variance. Together these lift the panel's statistical evidence:

	v0.3	v0.4
Cells WGeo-family wins on CRPS	12 / 12	12 / 12
Cells with vanilla DM p<0.05	1 / 12 (8%)	4 / 12 (33%)
Cells with residualised DM p_r<0.05	—	8 / 12 (67%)

Per-cell headline numbers, regime-conditional DM tables, and the full falsification verdict against docs/THEORY.md §4 are in docs/RESULTS_LONG.md. Methods-paper-style writeup in docs/RESEARCH_REPORT.md.

Install

The supported workflow uses uv (fast and reproducible). The package itself works under any Python ≥3.11.

git clone https://github.com/AccursedGalaxy/wasserstein-btc
cd wasserstein-btc
uv sync          # creates .venv with locked deps
uv run wbtc test # 53 tests, ~10 seconds

A PyPI release (pip install wbtc) is wired up via .github/workflows/publish-pypi.yml and ships on the next signed tag — see ROADMAP.md.

Quick start — CLI

uv run wbtc info                              # what data do I have?
uv run wbtc fetch                             # fetch / update default panel from Binance
uv run wbtc forecast BTC/USDT -H 5 --plot     # forecast & fan-chart PNG
uv run wbtc forecast BTC/USDT -H 5 --json     # JSON for scripting
uv run wbtc backtest --quick                  # fast single-symbol backtest
uv run wbtc backtest-long                     # full multi-asset (~30 min)
uv run wbtc extended-baselines                # HAR-RV/CAViaR/MS/FIGARCH/SV/BVAR vs WGeo on BTC (~2h)
uv run wbtc sweep                             # hyperparameter robustness

Quick start — Python

from wbtc import forecast, available_symbols, default_forecaster

available_symbols()
# ['BNB/USDT', 'BTC/USDT', 'ETH/USDT', 'SOL/USDT', 'XRP/USDT']

fc = forecast("BTC/USDT", horizon=5)
fc.median, fc.quantile(0.05), fc.quantile(0.95)
fc.to_dict()  # JSON-safe summary

# Pick a specific variant explicitly:
from wbtc import WassersteinGeodesicEWMA
fc = forecast("BTC/USDT", horizon=5,
              forecaster=WassersteinGeodesicEWMA(window=90, lookback=20))

default_forecaster(horizon) returns the recommended variant per horizon (see RESEARCH_REPORT.md §7).

What's novel

• Per-quantile time-regression on the W₂ manifold. The 1D-W₂-as- quantile-function isometry is textbook (Villani 2009 ch. 6); applying it to time-series tangent extrapolation of return distributions appears to be under-published. The closest published method (Saluzzi & Soize 2025, arXiv:2507.07570) uses a Koopman/EDMD-spectral approach with no regime adaptation, applied to housing prices.
• Cosine-curvature gate. Continuous, non-Markovian gating that blends geodesic extrapolation with a static-empirical fallback when consecutive tangent vectors become orthogonal. Pays off at h=1.
• Theil-Sen robust slope on the tangent. 29.3% breakdown point; robust to recent-history outliers without explicit regime modelling.
• Quantile-coordinate ensemble with GARCH. Convex combination in quantile-function space is an exact W₂-geodesic interpolation (McCann 1997) — not a moment-matched or kernel-mixed surrogate.

Documents

docs/
  THEORY.md           math (§2.6–2.8 are the v0.3 sections, §4 lists
                      explicit falsification criteria)
  RESEARCH_REPORT.md  paper-style writeup of the v0.3 contributions
  RESULTS_LONG.md     auto-regenerated 4-asset × 3-horizon evidence
  RESULTS.md          legacy v0.1 single-year report (superseded)
  INDEX.md            one-paragraph orientation to every doc
ROADMAP.md            v0.4 + v0.5 priorities (what would make it
                      competitive vs. production risk systems)
CONTRIBUTING.md       the conventions PRs must follow
CHANGELOG.md          v0.1 → v0.2 → v0.3 history

Honest limitations

• We have benchmarked against textbook baselines as headline (Static / RW / HS / GARCH-N / GARCH-t / GJR-GARCH-t across 4 assets × 3 horizons in docs/RESULTS_LONG.md) and against a broader named-econometric panel on BTC in docs/RESULTS_EXTENDED.md: HAR-RV (Corsi 2009), CAViaR-SAV (Engle-Manganelli 2004), 2-state Markov-switching Normal (Hamilton 1989), FIGARCH(1,d,0) (Baillie-Bollerslev-Mikkelsen 1996), AR(1) Stochastic Volatility (Taylor 1982 / Harvey-Ruiz-Shephard 1994 via Kalman QML), and a bivariate VAR+GARCH using BTC + ETH jointly. Any production-risk-system claim is still unsupported — this rounds out the academic panel.
• Daily-only. Intraday volatility dynamics are different.
• Univariate only. The 1D-W₂ isometry doesn't extend cleanly to higher dimensions; multivariate is a v0.5 research item.
• No trading P&L claim. Distributional-forecast quality is necessary but not sufficient for tradeable alpha.
• Heteroskedastic-dispersion variant (WGeo-Hetero) was a documented dead end — see RESEARCH_REPORT.md §4.4 for why (empirical-quantile-based dispersion already encodes the regime; multiplying by GARCH double-counts). The boundary is reusable.

Citation

If you use this software in academic work, please cite it. CITATION.cff is the structured form; the BibTeX-shaped quick form:

@software{wasserstein_btc_2026,
  author       = {Robin Bohrer (AccursedGalaxy)},
  title        = {wasserstein-btc: tangent-space Wasserstein-geodesic
                  distributional forecasting for crypto returns},
  version      = {0.4.0},
  year         = {2026},
  url          = {https://github.com/AccursedGalaxy/wasserstein-btc}
}

License

MIT.

Disclaimer

This is research code. Not financial advice. Falsification criteria are documented in docs/THEORY.md §4 and tested against the full long-horizon backtest in docs/RESULTS_LONG.md. Documented failures are in docs/RESEARCH_REPORT.md §4.2.