LOB Micro-Regime Early Detection — Summary

Overview
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This project studies early detection of latent instability in limit order books (LOB) before observable liquidity stress.

A causal three-regime model is used:
- Regime 0: Stable
- Regime 1: Latent build-up (hidden deterioration)
- Regime 2: Stress (observable disruption)

The transition from build-up to stress occurs with a delay, enabling evaluation of early detection.

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Method
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The proposed detector combines:
- Probabilistic instability (HMM posterior entropy)
- Temporal drift (spread, depth dynamics)
- Structural signals (depth erosion, order flow)

Final detection uses:
- MAX-trigger fusion across channels
- Rising-edge detection (onset of instability)
- Early-detection constraint (ensuring signals precede stress)

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Evaluation Metrics
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- Lead-time: Δ = σ − τ (positive = early detection)
- Precision: fraction of detections occurring before stress
- Coverage: fraction of stress events detected early

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Results
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Adaptive Trigger (final method):
- Mean Δ (lead-time): +18.62 steps
- Precision: 100%
- Coverage: 52.6%

Other variants:
- Model: Δ = +14.95 | Precision = 100% | Coverage = 43.2%
- Multi-Trigger: Δ = +13.15 | Precision = 100% | Coverage = 28.1%

Baselines:
- Imbalance: Δ = -24.84 | Precision = 54.9% | Coverage = 78.7%
- Volatility: Δ = -32.02 | Precision = 45.5% | Coverage = 43.3%

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Key Findings
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- Latent instability signals exist prior to observable stress.
- Standard baselines are reactive (negative lead-time).
- Trigger-based detection enables strictly positive lead-time.
- A trade-off exists between early detection and coverage.
- Depth erosion and entropy are the dominant early indicators.

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Reproducibility
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- Implemented in Python (NumPy, scikit-learn, hmmlearn)
- Tested on:
  - Google Colab (NVIDIA T4)
  - Apple MacBook (M4)

All figures and results are generated from the provided pipeline.