$ cat methodology.md

Conformal prediction is the framework we are building toward: a distribution-free method for constructing prediction sets with finite-sample coverage properties. Given a calibration set {(X_i, Y_i)}_{i=1}^n and a new test point X_{n+1}, the conformal prediction set C(X_{n+1}) satisfies P(Y_{n+1} ∈ C(X_{n+1})) ≥ 1 - α under the exchangeability assumption. No parametric distributional assumptions are required. Our roadmap includes three methods — StandardCP, MondrianCP, and CQR. No conformal model is currently in production; all figures shown are illustrative samples.

StandardCP: Split conformal with nonconformity scores s_i = |Y_i - μ̂(X_i)| for regression or 1 - π̂_y(X_i) for classification. The prediction set includes all labels y where the score is below the (1-α)(1+1/n) quantile of calibration scores. MondrianCP: Group-conditional conformal that partitions the calibration set by regime labels (EXPANSION/CONTRACTION/TRANSITION) and computes per-group thresholds. is designed to provide coverage properties within each group, not just marginally (roadmap). CQR: Trains quantile regressors at levels α/2 and 1-α/2, then conformally calibrates the residuals, designed to provide finite-sample coverage (roadmap), producing intervals that adapt to local variance.

The Hamilton filter regresses Y_t on Y_{t-h} (typically h=24 months) to extract the cyclical component as the residual: ε_t = Y_t - β̂₀ - β̂₁Y_{t-h}. This avoids the spurious cycle artifacts and endpoint instability of the Hodrick-Prescott filter. The residuals preserve the spectral properties of the underlying cyclical dynamics without introducing phase shifts.

The Lomb-Scargle periodogram estimates spectral power P(ω) at angular frequency ω from unevenly sampled data. We apply it to Hamilton-filtered residuals to identify the dominant cycle frequency. The fitted sinusoid f(t) = A·sin(ωt + φ) parameterizes the cycle position into four quadrants: TROUGH (φ ∈ [π, 3π/2)), RECOVERY (φ ∈ [3π/2, 2π)), PEAK (φ ∈ [0, π/2)), CONTRACTION (φ ∈ [π/2, π)). R² of the sinusoidal fit quantifies cycle regularity.

Net S-D is a composite z-score: z(supply) - z(demand). Supply components (e.g., Fed total assets, M2, bank reserves) are individually z-scored over a trailing window and averaged. Demand components (e.g., Treasury general account, RRP facility balance) are similarly z-scored, optionally sign-inverted, and averaged. The composite is computed monthly from 1998–present. Year-over-year changes in Net S-D drive regime classification: sustained positive ΔNet S-D → EXPANSION, sustained negative → CONTRACTION, ambiguous → TRANSITION.

Regime labels are assigned based on year-over-year ΔNet S-D with hysteresis thresholds to prevent chattering. The classification uses a 3-state model: EXPANSION (ΔNet S-D > +σ for ≥3 consecutive months), CONTRACTION (ΔNet S-D < -σ for ≥3 consecutive months), TRANSITION (otherwise). On our roadmap, MondrianCP would leverage these regime labels for group-conditional conformal inference, designed to provide coverage properties stratified by market state. Regime durations range from 4 to 36 months historically.

GET /api/quant/regime-nowcast serves the current m02-nowcast snapshot (Σpᵢ = 1 enforced by DB CHECK). The Quant Lab regime tab renders the distribution with a staleness chip; hit-rates in GET /api/signal/hit-rate score the nowcast timeline against realized forward returns with Wilson 95% CIs.

Temporal cross-validation with purged groups: fold boundaries are determined by time-sorted indices with a gap buffer equal to the forecast horizon. Within each fold, the model is trained on data before the purge boundary and evaluated on data after it. Coverage is measured as the fraction of test points whose true value falls within the conformal prediction set. We target 90% coverage (α=0.10) with an acceptance band of [85%, 95%]. Slots are classified as ON_TARGET (85-95%), OVERCOVERING (>95%), or UNDERCOVERING (<85%).

Macro regime context improves intraday alpha through three mechanisms: (1) Directional bias: BTC 12-month returns average +127% in EXPANSION vs -31% in CONTRACTION regimes since 2015, providing a statistical prior for trade direction. (2) Volatility regime: VIX z-score > 1.5 correlates with 2.3x average true range expansion, affecting position sizing and stop placement. (3) Correlation regime: Cross-asset correlations shift significantly between regimes (BTC-SPX correlation: +0.62 in contraction vs +0.21 in expansion), affecting portfolio hedging and pair trades.

The FRED refresh map covers 11 series ids (WALCL, M2SL, WTREGEN, RRPONTSYD, TOTRESNS, DGS5, SOFR, BAMLH0A0HYM2, BAMLC0A0CAA, NAPM, VIXCLS); 9 carry data in the March-2026 snapshot. Market data from Yahoo Finance covers 8 core assets at daily resolution. Derived features include z-scores (trailing 36-month window), year-over-year changes, Hamilton-filtered residuals, and Lomb-Scargle cycle parameters.

The `rebel` module is automatically injected into the PYTHONPATH of the secure execution environment. Methods: • `rebel.plot(name: str, values: list, color: str)`: Emits a standard JSON payload (`{"overlay_chart": ...}`) intercepted by the frontend Terminal. Maps the vector to the active conformal prediction chart using the global timeline. • `rebel.promote_to_hub(slot: str, name: str, values: list, regime: str, confidence: float)`: Extends the plot payload with `promote_to_hub: True` and a target `slot` (L5-L12). The frontend intercepts this to dynamically populate the `FormulaDataContext`, persisting the module via `localStorage` to survive page navigation to `/intelligence`.