The market as a trajectory on the 2-Wasserstein manifold of returns.
wbtc forecasts the conditional distribution of crypto log-returns by treating the empirical return distribution as a point on the 2-Wasserstein manifold of probability measures, and extrapolating along geodesics in quantile-function coordinates. Walk-forward, strictly-proper-scored, and benchmarked against six classical baselines plus six named econometric comparators.
Method families
Every forecaster obeys the same fit/predict protocol and produces a quantile function on a shared grid. The headline contribution is the WGeo family.
Headline · best WGeo vs best baseline
Walk-forward CRPS over a 6.75-year, multi-asset out-of-sample window. Negative Δ means the WGeo family wins. p is the classic Diebold-Mariano (1995) two-sided p-value; pr is the v0.4 residualised DM (Giacomini-White-style augmented test that projects out shared volatility-clustering noise via |y|, y², and peer-method losses — see THEORY.md §2.10).
| Asset | h | n | Best WGeo | CRPS | Best baseline | CRPS | Δ | DM | p | DMr | pr |
|---|
Cumulative CRPS — the audit trail
The cumulative loss curve over the entire walk-forward. A method that stays beneath another for years is genuinely better; one that crosses over only briefly is noise.
Cumulative CRPS over the walk-forward — lower is better. A method that stays beneath another for years is genuinely better.
Mean CRPS by method
Same (asset, h) as above — sorted best→worst. Use Δ-vs-Static to see the differences that look identical at four decimal places.
DM significance vs Static
Diebold-Mariano (Newey-West HAC) — each WGeo variant vs Static. Green = WGeo significantly better, red = significantly worse, grey = tie. Dashed lines mark the two-sided 5% / 10% critical values.
Extended econometric panel · BTC
v0.4 — the regime-aware WGeo ensemble against named comparators from adjacent econometric families. Walk-forward CRPS, same protocol as the headline.
Mean CRPS · sorted best→worst
Cumulative CRPS · differences become visible in Δ mode
Hyperparameter robustness
Mean CRPS over a 4 × 4 grid of window (training tail) × lookback (geodesic tangent fit). The objective is to make the bright corner small and the surface flat.
Early epoch · 2019–2022
The "selection" window — used for picking defaults.
Late epoch · 2023–2026
The "verification" window — must not be looked at during selection.
The underlying markets
Daily candles + log-returns for each asset. This is the raw object the forecaster receives.
Provenance & reproducibility
Every chart on this page is regenerable from the same git commit, the same parquet files, the same library versions.