---

name: signal-audit description: Measure predictive information content of signals using mutual information, correlation, and optimal lag analysis. Use before building models, when adding data sources, debugging signal decay, or selecting features. Covers MI estimation, regime-conditional analysis, and decay tracking. requires:

• measurement-infrastructure user-invocable: false

---

Signal Audit Skill

Purpose

Systematically measure the predictive information content of all available signals before building models. This prevents wasting effort on low-value features and identifies high-value signals you might be ignoring.

When to Use

• Before building any new predictive model
• When adding a new data source (cross-exchange feed, new API field)
• Quarterly review of signal value decay
• Debugging why a model stopped working
• Deciding which features to include in a model

Prerequisites

• measurement-infrastructure implemented (for outcome data)
• Historical market data with candidate signals
• Defined prediction targets

---

Core Concept: Mutual Information

Mutual information measures how many bits of information signal X provides about target Y:

I(X; Y) = H(Y) - H(Y|X)

Where H is entropy.

Key properties:

• I(X; Y) ≥ 0 (always non-negative)
• I(X; Y) = 0 if and only if X and Y are independent
• Works for non-linear relationships (unlike correlation)
• Units are bits (or nats if using natural log)

---

Signal Catalog

Book-Derived Signals

• Basic: spread_bps, mid_price
• Imbalance: microprice_imbalance (L1), book_imbalance_l5 (top 5), book_pressure (weighted depth asymmetry)
• Depth: depth_at_1bps, depth_at_5bps, depth_at_10bps
• Shape: book_slope_bid, book_slope_ask (depth increase rate away from mid)

Trade-Derived Signals

• Volume imbalance: trade_imbalance_{1s,10s,60s} (net signed volume)
• Intensity: trade_arrival_rate, volume_rate
• Size distribution: avg_trade_size, trade_size_std, large_trade_count_1m (> 2 sigma)
• Aggression: aggressor_imbalance

Hyperliquid-Specific Signals

• Funding: funding_rate, funding_rate_change_{1h,8h}, predicted_funding_rate, time_to_funding_settlement_s
• Open Interest: open_interest, open_interest_change_{1m,5m,1h}, oi_momentum
• Vault: hlp_vault_position

Cross-Exchange Signals

• Binance: binance_mid, binance_spread_bps, binance_hl_basis_bps
• Lead indicators: binance_return_{100ms,500ms,1s}
• Volume ratio: binance_volume_ratio (Binance / HL)

Composite Signals

• Interactions: funding_x_imbalance, oi_x_funding, basis_x_imbalance
• Momentum: price_momentum_{1m,5m}, volume_momentum

See implementation.md for full struct definitions.

---

Prediction Targets

• Direction: PriceDirection{1s,10s,60s} -- sign of future return
• Magnitude: AbsReturn{1s,10s}, Volatility1m
• Fill-related: FillWithin{1s,10s}, TimeToNextFill
• Adverse selection: AdverseOnNextFill, InformedFlow
• Regime: RegimeTransition (will regime change in next minute?)

---

Mutual Information Estimation

k-NN Estimator (Kraskov et al.)

For continuous variables, use the k-nearest-neighbor estimator (estimate_mutual_information). Normalizes inputs to [0,1], builds k-d trees in joint and marginal spaces, then computes MI via digamma functions on neighbor counts. Typical k = 3-10.

For Binary Targets

Use the simpler binned estimator (estimate_mi_binary_target). Bins the continuous variable, counts joint/marginal frequencies, and computes MI from the frequency table.

See implementation.md for full code of both estimators.

---

Signal Analysis Framework

SignalAnalysisResult captures per-signal metrics:

Field	Description
mutual_information_bits	Raw MI in bits
mutual_information_normalized	MI / H(Y), fraction of target entropy explained
correlation, correlation_abs	Linear relationship (for comparison)
auc_roc	ROC AUC for binary targets
optimal_lag_ms, mi_at_optimal_lag	Best lag and MI at that lag
mi_by_regime, regime_variance_ratio	Per-regime MI and max/min ratio
mi_trend_30d	Stationarity trend

analyze_signal() computes MI, correlation, optimal lag (candidate lags: -500ms to +500ms), and per-regime MI (min 100 samples per regime). find_optimal_lag() sweeps candidate lags and returns the one with highest MI.

See implementation.md for full code.

---

Signal Audit Report

generate_signal_audit_report() analyzes all signals against a target, sorts by MI descending, and produces a table with actionable insights. The report flags: (1) highest-MI signal, (2) regime-conditional signals (variance ratio > 2x), (3) signals with 20%+ more MI at a lag, (4) high-correlation but low-MI signals (possibly spurious).

See implementation.md for full code.

Example Report Output

=== Signal Audit Report ===
Target: PriceDirection1s

Signal                      MI (bits)  Corr    Opt Lag   Regime Var
─────────────────────────────────────────────────────────────────────
binance_return_100ms        0.0890     0.31    -150ms    2.3x
trade_imbalance_1s          0.0670     0.24       0ms    1.4x
microprice_imbalance        0.0450     0.19       0ms    1.2x
funding_x_imbalance         0.0410     0.15       0ms    3.1x
open_interest_change_1m     0.0230     0.08       0ms    1.1x
book_pressure               0.0180     0.11       0ms    1.3x
funding_rate                0.0120     0.05       0ms    1.8x

ACTIONABLE INSIGHTS:
1. binance_return_100ms has highest MI (0.089 bits) - prioritize if not already used
2. funding_x_imbalance has 3.1x higher MI in some regimes - consider regime conditioning
3. binance_return_100ms has 20%+ more MI at -150ms lag - incorporate lag in feature

---

Signal Quality Thresholds

Typical thresholds:

Parameter	Typical Value	Purpose
min_mi_bits	0.01	Minimum MI to include in model
min_samples	1000	Minimum samples for reliable MI estimate
max_regime_variance	3.0	Above this, require regime conditioning
min_correlation	0.05	Sanity check floor

filter_signals() keeps signals above MI and correlation thresholds. flag_regime_conditional() flags signals with regime variance ratio above threshold.

See implementation.md for full code.

---

Tracking Signal Decay

Signals lose value over time as:

• Other participants discover them
• Market structure changes
• Regime shifts

compute_signal_decay() fits a linear regression on historical MI values over time and computes a half-life (days until MI drops 50%). Action thresholds:

• < 30 days: URGENT -- signal decaying rapidly, investigate or replace
• < 90 days: WARNING -- monitor closely
• >= 90 days: OK -- signal stable

See implementation.md for full code.

---

Dependencies

• Requires: measurement-infrastructure (for outcome data), historical market data
• Enables: All model skills (by identifying which features to use)

Common Mistakes

1. Using correlation instead of MI: Correlation misses non-linear relationships
2. Not checking lag: Some signals lead the target and are more valuable at a lag
3. Ignoring regime conditioning: A signal useless overall might be gold in specific regimes
4. Not tracking decay: Signals that worked last year might be worthless now
5. Too few samples: MI estimation needs 1000+ samples for reliability

Next Steps

After signal audit:

1. Select top signals for your target (MI > 0.01 bits)
2. Flag regime-conditional signals for special handling
3. Incorporate optimal lags into feature engineering
4. Read the relevant model skill to build the predictor
5. Set up decay tracking for production monitoring

Supporting Files

• implementation.md -- All Rust code: signal structs, MI estimators, analysis framework, report generation, quality thresholds, decay tracking