DLI スケール不変性 — ハイブリッド変換補遺

⚠️ SUPERSEDED (2026-05-05). This note describes the retired linear weighted-average DLI (85/5/5/5 group weights, z-score transforms, forward-return backtests). The current engine uses CISS-style quadratic aggregation — see 2026-05-DLI-CISS.md. Kept for historical context only.

DLI scale invariance — hybrid transform addendum

Decision

Group D indicators (VIX, broad dollar index, 10-year real yield) now use a 2-year rolling percentile rank in place of the 10-year robust z-score. Groups A, B, C continue to use z-scores.

DLI = 0.85·A_zscore + 0.05·B_zscore + 0.05·C_zscore + 0.05·D_percentile_zequiv

Where the percentile is rescaled to z-equivalent units (p − 50) / 16 so it can be averaged with the other groups in the same magnitude space.

Why

The original z-score-only DLI implicitly assumes stable distribution. But the underlying flow indicators have scaled by an order of magnitude:

A 10-year rolling MAD adapts somewhat, but z-scores still mix regime epochs and outliers in price-feedback indicators (VIX especially) blow up the signal.

The empirical proof on 11-year SPX/QQQ/IWM/TLT/HYG/GOLD universe at 60d horizon:

Pure-percentile breaks rate-sensitive (TLT) and credit (HYG) assets because their relationship to liquidity is sensitive to magnitude — a real-yield z-score of +3 means something materially different from +2 for long-duration bonds.

Pure-z keeps GOLD inverted because of VIX/dollar-index outlier feedback.

The hybrid keeps magnitude information where it matters (A/B/C) and compresses outliers where they're mechanical feedback (D). Result: every asset's 60d Δavg improves vs pure-Z, GOLD specifically flips from −1.56%\* to +0.55%.

Implementation

lib/indicators/config.ts:

export const DLI_GROUP_CONFIG = {
  A: { weight: 0.85, transform: 'z',          ... },
  B: { weight: 0.05, transform: 'z',          ... },
  C: { weight: 0.05, transform: 'z',          ... },
  D: { weight: 0.05, transform: 'percentile', ... },
};
export const DLI_PERCENTILE_WINDOW_DAYS = 730;  // 2y rolling window

lib/regime/engine.ts:

• resolveIndicatorSignal(group, id, series, date) looks up the indicator's z-score with staleness tolerance, then either returns the tightness-aligned z directly (if transform === 'z') or computes its rank percentile within the rolling 730-day window and rescales via (p − 50) / 16.
• computeSubIndex, computePreviousSubIndex, and calculateDLIHistory Pass 1 all funnel through resolveIndicatorSignal so the transform flag is honored uniformly.

The 30-observation minimum protects early-window dates from spurious low-sample percentiles.

What this does NOT change

• Group weights (still 85/5/5/5)
• Regime cuts (still p20/p80 on the unified DLI level)
• Forward-window backtest design (20d + 60d shown in UI)
• A-momentum kicker (still off, DLI_A_MOMENTUM_COEF = 0)

Validation summary

5y on-page display will still look weak (2021-2026 is the structurally hardest sub-window), but the underlying formula is now:

1. Scale-invariant on D — VIX of 30 in 2018 vs VIX of 30 in 2024 contribute the same percentile signal regardless of which decade's distribution we anchor against
2. Magnitude-preserving on A/B/C — Fed BS shrinking by $200B in a quarter still pushes the z-score the appropriate amount
3. Lower outlier dependency — A single VIX spike to 80 (March 2020 / Aug 2024) no longer single-handedly drives DLI to +4σ; it gets capped at the 100th percentile = +3.125 z-equivalent

How to re-validate

1. python3 /tmp/dli_pct.py (or recreate from this addendum's logic) on whatever indicator-z-score data is available
2. Compare: pure-z A85/5/5/5 vs hybrid A85/5/5/5
3. The hybrid should improve all major risk assets at 60d horizon by 10-50bp, with GOLD as the standout (≈ +200bp)