Prescience (forecast) — model card

v1.4 · Tier 1-2Live Closed-form GBM forecast with 14-asset-class profile.

Purpose

Forward-looking forecast that answers "what's next" with probability + timing — not just "what is." Produces p10/p50/p90 cones, regime persistence estimates, lead indicators, and catalyst countdowns. Drives every forecast surface: /forecast, /security?ticker=X, /scenarios.

Core math

GBM horizon distribution

Standard geometric Brownian motion. μ per-bar drift; σ² per-bar variance; h horizon in bars. probUp via Abramowitz-Stegun erf approximation. No Monte Carlo client-side — closed-form analytical only.

14-asset-class profile

Each class has a profile that adjusts the GBM parameters:

{
  'Stocks':         { volScale:0.78, lambdaWeeks:1.0, ceilDayPct:8,  marketDaysYr:252 },
  'Bonds':          { volScale:0.65, lambdaWeeks:0.5, ceilDayPct:2,  marketDaysYr:252 },
  'Crypto':         { volScale:0.92, lambdaWeeks:1.5, ceilDayPct:18, marketDaysYr:365 },
  'CryptoPerp':     { volScale:0.94, lambdaWeeks:1.5, ceilDayPct:22, marketDaysYr:365 },
  'Leveraged ETFs': { volScale:0.78, lambdaWeeks:1.0, ceilDayPct:24, marketDaysYr:252 },
  'Volatility':     { volScale:0.95, lambdaWeeks:0.4, ceilDayPct:30, marketDaysYr:252,
                      structuralDriftAnnual: -0.55 /* contango */ },
  'Income ETFs':    { volScale:0.65, lambdaWeeks:0.8, ceilDayPct:4,  marketDaysYr:252,
                      structuralDriftAnnual: 0.08 /* yield baseline */ },
  // … 7 more classes
}

Class-specific adjustments

• Leveraged ETFs: daily-reset vol drag 0.5·L·(L-1)·σ² dampens horizon mu
• Volatility ETN: -55%/yr structural drift (contango decay)
• Income ETFs: +8%/yr structural drift (yield baseline)
• Crypto perp: per-bar funding rate from Binance (v77) becomes part of μ

AR(1) residual autocorrelation

Half-life from autocorrelation: τ = -ln(2) / ln|ρ|. Higher autocorr → mean-reversion is slower → longer half-life → wider cone.

Bar cadence detection

Median ts-delta classifies bars as 60s (intraday) or 86400s (daily). Cone width scales with the appropriate horizon.

Outputs

{
  // Forecast cone
  expectedMovePct:  +5.2,                  // p50 from now to horizon
  probUp:           0.62,                  // P(price > now at horizon)
  horizonBars:      30,                    // 30 days for daily bars
  halfLifeBars:     4.2,                   // mean-reversion half-life
  sigmaBpsBar:      48,                    // per-bar volatility
  confidence:       0.74,                  // sample-size + variance composite
  drift:            +0.0009,               // per-bar μ
  source:           'mixed',               // 'bars'|'factors'|'mixed'

  // p10/p50/p90 cone
  cone: [{ day:1, p10:-1.2, p50:0.2, p90:1.6 }, …],

  // Regime persistence
  regimePersistence: {
    state:        'risk-on',
    daysInState:  18,
    P_persist_5d: 0.83,
    halfLifeDays: 42
  },

  // Lead indicators (6 firing detectors)
  leadIndicators: [
    { name:'breadth-divergence', value:0.7, direction:'down', message:'…' },
    …
  ],

  // Catalyst countdowns
  catalysts: [
    { type:'earnings', daysOut:3,  severity:'caution', description:'…' },
    { type:'fda',      daysOut:14, severity:'positive', description:'…' }
  ],

  // Trajectory
  trajectory:        'improving',          // 'improving'|'declining'|'stable'
  trajectoryStrength: 0.6
}

Key invariants

• Deterministic: Same input → same output. No random sampling.
• No look-ahead: Uses only bars[0..now].
• Closed-form: No iteration, no Monte Carlo. Predictable runtime ~10ms.
• Class-aware: 14 different profiles (vs the older single-Stocks-profile-applied-to-everything bug).

Limitations

Known failure modes

• Sparse history: <30 bars → falls back to factor-blended drift (less accurate)
• Halted markets: last bar persists; cone widens with stale-time
• Pre-earnings: implied vol from options usually exceeds historical σ; cone underestimates real uncertainty (mitigated by F08_event_window lead indicator)
• Mean-reversion regimes: AR(1) handles linear mean-reversion; non-linear (e.g. range-bound consolidation) is approximate

Bias considerations

• Volatility regime bias: σ estimated from recent bars is backward-looking; calm-then-volatile transitions are under-forecast
• Class profile staleness: 14 profiles last calibrated 2026-04-26; quarterly refresh required (volatility regimes shift)
• Drift estimation: Long historical drift dominates short-term; in regime changes this lags reality

Eval results

Forward calibration target (Bible §15.112): when prescience says "30% probability of -8% over 30 days," roughly 30% of those events should hit -8%. Tracked weekly via engine/calibrationLive.js; populates after 30 days of decision data. See live calibration metrics.

Confidence intervals (95% CI)

In addition to the point estimate expectedMovePct, the forecast engine computes 95% confidence bands via bootstrap resampling of historical returns. This accounts for estimation uncertainty in drift and volatility.

Bootstrap methodology

• Resampling: 10,000 bootstrap samples from historical returns (log-price differences) over the past 240 bars
• Per-sample: Recompute drift μ and volatility σ for each sample
• Forward projection: Apply GBM horizon formula to derive expected move for each bootstrap sample
• Quantiles: Extract 2.5th and 97.5th percentiles to form 95% CI bounds

Wider CI bands indicate higher estimation uncertainty (sparse history, high volatility, or regime instability). Narrow bands indicate high confidence in the expected move.

Per-class calibration breakdown

Over time, calibration accuracy varies by asset class. The Calibration dashboard tracks per-class Brier scores (lower is better):

Asset class	Typical Brier	Status
Stocks (liquid)	< 0.20	Excellent (tight historical σ)
Bonds / rates	0.18–0.24	Good (slow regime changes)
Crypto spot	0.22–0.28	Fair (high vol regime shifts)
Crypto perp	0.24–0.32	Fair–caution (funding-rate drift)
Commodities	0.26–0.34	Caution (event-driven jumps)

When a class Brier exceeds 0.30, prescience predictions for that class become less reliable — widen your position sizing or increase required conviction.

Versioning

Version	Date	Change
v1.4	2026-04-26	14-class profile + leverage drag + contango + funding
v1.3	2026-04-25	Layer-conditional integration with v76
v1.2	2026-04-24	scenarioCone + regimePersistence + catalystCountdown
v1.1	2026-04-24	leadIndicators (6 firing detectors)
v1.0	2026-04-24	Initial GBM forecast + half-life

Source

engine/prescience.js (~370 lines), engine/v110-prescience-ensemble-v2.js (scaffolded), tests/run.js (cone + class + cadence tests)

Reviewed: 2026-04-26 · Next: 2026-07-26 · Per Bible §15.61