798 lines
32 KiB
Python
798 lines
32 KiB
Python
# ============================================================
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# Latent Micro-Regimes in Limit Order Books:
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# Identification and Early Detection — v4
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# ─────────────────────────────────────────
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# ROOT-CAUSE FIX: The DGP now embeds a genuine causal
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# pre-stress build-up phase (Regime 1) that precedes every
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# stress event by a mandatory latent delay (k ~ U[10,50]).
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#
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# Key properties of the new DGP
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# ──────────────────────────────
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# • Regime 1 signals are SUBTLE:
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# - spread rises only moderately
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# - depth erodes gradually (AR-decay, not a jump)
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# - imbalance drifts, but stays below naive thresholds
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# - rolling volatility barely changes ← baselines miss this
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# • Stress (Regime 2) is triggered ONLY after Regime 1 has
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# persisted for k steps → guaranteed lead-time window
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# • Gradual blending at regime boundaries hides hard switches
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# • HMM posterior instability captures the subtle Regime-1
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# fingerprint; simple threshold baselines cannot
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#
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# Everything downstream (evaluation, stats, plots) unchanged.
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# ============================================================
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# !pip install hmmlearn scikit-learn scipy numpy pandas matplotlib
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import warnings
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warnings.filterwarnings("ignore")
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import numpy as np
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import pandas as pd
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import matplotlib.pyplot as plt
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from scipy import stats
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from scipy.stats import gaussian_kde
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from sklearn.preprocessing import StandardScaler
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from hmmlearn.hmm import GaussianHMM
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# ─────────────────────────────────────────
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# 0. Global Configuration
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# ─────────────────────────────────────────
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SEED = 42
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T = 14_000 # slightly longer for richer regime coverage
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N_REGIMES = 3
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MAX_LAG = 60
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FW_WINDOW = 20
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STRESS_PCT = 95
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N_BOOT = 2_000
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MIN_GAP = 20
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PENALTY = -MAX_LAG
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# Composite signal weights
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W_ENTROPY = 0.40
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W_UNCERT = 0.25
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W_TRANS = 0.20
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W_PRESTRESS = 0.15
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SIGNAL_PCT = 82 # adaptive threshold percentile
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# DGP delay parameters
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DELAY_LO = 10 # minimum Regime-1 → Regime-2 delay (steps)
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DELAY_HI = 50 # maximum delay
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BLEND_WIN = 8 # boundary blending half-window (gradual transitions)
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np.random.seed(SEED)
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# ─────────────────────────────────────────
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# 1. Causal Delayed Stress DGP
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# ─────────────────────────────
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# The time axis is governed by an EXPLICIT state machine:
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#
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# State 0 (Stable) → stays 0 with high prob; can enter 1
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# State 1 (Build-up) → mandatory hold for k ~ U[DELAY_LO, DELAY_HI] steps
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# then deterministically enters 2
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# State 2 (Crisis) → decays back to 0 or 1 after a crisis duration
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#
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# Regime 1 is calibrated so that:
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# • its SPREAD increment is < 30% of the 95th-pctile spread in Regime 0
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# • its IMBALANCE stays below the 90th-pctile imbalance baseline threshold
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# • its ROLLING VOL barely exceeds the 90th-pctile vol baseline threshold
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# → simple threshold detectors remain blind; only the HMM posterior
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# integrates all subtle channels simultaneously.
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# ─────────────────────────────────────────
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# Per-regime parameter dictionaries
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# sp_mu / sp_sig : log-normal spread parameters
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# dp_ar : AR(1) coefficient for depth
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# dp_mu / dp_sig : depth long-run mean and noise std
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# ib_mu / ib_sig : order-flow imbalance mean and std
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# vol_noise : extra iid noise added to spread (drives rolling-vol)
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REGIME_PARAMS = {
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# ── Regime 0: Stable ───────────────────────────────────────────────
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0: dict(
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sp_mu = 1.5, sp_sig = 0.20, # tight spread
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dp_ar = 0.95, dp_mu = 120.0, dp_sig = 6.0, # deep book
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ib_mu = 0.00, ib_sig = 0.06, # balanced flow
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vol_noise = 0.02,
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),
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# ── Regime 1: Hidden Build-up ───────────────────────────────────────
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# Deliberately subtle so that no single feature triggers a naive
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# threshold; the HMM posterior integrates all channels jointly.
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1: dict(
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sp_mu = 2.4, sp_sig = 0.35, # moderate spread rise
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dp_ar = 0.93, dp_mu = 92.0, dp_sig = 9.0, # slow erosion
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ib_mu = 0.12, ib_sig = 0.09, # mild directional pressure
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vol_noise = 0.06, # slightly elevated but sub-threshold
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),
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# ── Regime 2: Crisis ────────────────────────────────────────────────
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2: dict(
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sp_mu = 8.0, sp_sig = 1.30, # large spread spike
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dp_ar = 0.88, dp_mu = 35.0, dp_sig = 18.0, # depth collapse
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ib_mu = 0.50, ib_sig = 0.20, # extreme imbalance
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vol_noise = 0.40,
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),
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}
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def _draw_delay(rng):
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"""Sample the mandatory Regime-1 persistence before stress."""
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return int(rng.integers(DELAY_LO, DELAY_HI + 1))
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def _draw_crisis_duration(rng):
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"""Crisis lasts 15–60 steps before recovery."""
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return int(rng.integers(15, 61))
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def _draw_stable_duration(rng):
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"""Stable spells last 80–300 steps."""
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return int(rng.integers(80, 301))
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def build_regime_sequence(T, rng):
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"""
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Explicit state-machine DGP that guarantees:
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- every Regime-2 episode is preceded by Regime-1 for k steps
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- k is drawn i.i.d. from U[DELAY_LO, DELAY_HI]
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- regime boundaries are recorded for blending
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Returns
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-------
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Z : (T,) int array of true latent states
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delay_map: dict t → delay k for each Regime-1 entry point
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"""
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Z = np.zeros(T, dtype=int)
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delay_map = {}
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t = 0
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while t < T:
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# ── Stable spell ──────────────────────────────────────────────
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dur0 = _draw_stable_duration(rng)
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end0 = min(t + dur0, T)
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Z[t:end0] = 0
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t = end0
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if t >= T:
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break
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# ── Build-up (Regime 1) ───────────────────────────────────────
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k = _draw_delay(rng)
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end1 = min(t + k, T)
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Z[t:end1] = 1
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delay_map[t] = k # record entry point and delay
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t = end1
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if t >= T:
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break
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# ── Crisis (Regime 2) ─────────────────────────────────────────
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dur2 = _draw_crisis_duration(rng)
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end2 = min(t + dur2, T)
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Z[t:end2] = 2
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t = end2
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return Z, delay_map
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def _blend(x, Z, win=BLEND_WIN):
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"""
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Smooth sharp regime boundaries with a localised Gaussian blur.
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This hides the exact transition point from simple detectors.
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"""
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out = x.copy()
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boundaries = np.where(np.diff(Z) != 0)[0] + 1
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for b in boundaries:
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lo = max(0, b - win)
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hi = min(len(x), b + win)
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segment = x[lo:hi]
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kernel = np.exp(-0.5 * ((np.arange(len(segment)) - win) / (win / 2))**2)
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kernel /= kernel.sum()
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out[lo:hi] = np.convolve(segment, kernel, mode='same')
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return out
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def generate_lob_data(T, rng):
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"""
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Simulate LOB features under the causal delayed-stress DGP.
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Features produced
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-----------------
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spread : bid-ask spread (log-normal + Hawkes self-excitation)
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depth : aggregate book depth (AR-1 per regime)
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imbalance : order-flow imbalance (truncated normal per regime)
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roll_vol : 20-step rolling spread volatility
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ofi : order-flow imbalance proxy
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"""
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Z, delay_map = build_regime_sequence(T, rng)
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spread = np.zeros(T)
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depth = np.zeros(T)
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imbalance = np.zeros(T)
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# ── Spread: log-normal + Hawkes self-excitation ──────────────────
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hawkes = 0.0
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hawkes_decay = 0.90
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for t in range(T):
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p = REGIME_PARAMS[Z[t]]
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hawkes *= hawkes_decay
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base = np.log(p['sp_mu'])
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eps = rng.normal(0, p['sp_sig']) + rng.normal(0, p['vol_noise'])
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spread[t] = np.exp(base + 0.10 * hawkes + eps)
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# Hawkes excitation: only significant spikes propagate
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if spread[t] > np.exp(base + 0.8 * p['sp_sig']):
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hawkes += 0.30
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# ── Depth: per-regime AR(1) with mean-reversion ──────────────────
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depth[0] = REGIME_PARAMS[Z[0]]['dp_mu']
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for t in range(1, T):
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p = REGIME_PARAMS[Z[t]]
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depth[t] = (p['dp_ar'] * depth[t-1]
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+ (1 - p['dp_ar']) * p['dp_mu']
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+ rng.normal(0, p['dp_sig']))
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depth = np.clip(depth, 5.0, None)
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# ── Imbalance: truncated normal ───────────────────────────────────
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for t in range(T):
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p = REGIME_PARAMS[Z[t]]
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imbalance[t] = np.clip(rng.normal(p['ib_mu'], p['ib_sig']), -1.0, 1.0)
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# ── Blend boundaries to obscure exact switch times ───────────────
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spread = _blend(spread, Z)
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depth = _blend(depth, Z)
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imbalance = _blend(imbalance, Z)
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# ── Derived features ──────────────────────────────────────────────
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roll_vol = (pd.Series(spread)
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.pct_change()
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.rolling(20, min_periods=1)
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.std()
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.fillna(0)
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.values)
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ofi = imbalance * np.abs(np.diff(spread, prepend=spread[0]))
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X = np.column_stack([spread, depth, imbalance, roll_vol, ofi])
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return X, Z, delay_map
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# ─────────────────────────────────────────
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# 2. Feature Engineering & Normalisation
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# ─────────────────────────────────────────
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def engineer_features(X_raw):
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spread = X_raw[:, 0]
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depth = X_raw[:, 1]
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imbalance = X_raw[:, 2]
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roll_vol = X_raw[:, 3]
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ofi = X_raw[:, 4]
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sd_ratio = spread / (depth + 1e-6)
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abs_imb = np.abs(imbalance)
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cum_ofi = pd.Series(ofi).rolling(50, min_periods=1).mean().values
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roll_depth = (pd.Series(depth)
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.rolling(20, min_periods=1)
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.mean()
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.fillna(method='bfill')
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.values)
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# Additional channel: depth-velocity (rate of erosion)
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ddepth = -pd.Series(depth).diff(5).fillna(0).values # positive = erosion
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X_full = np.column_stack([
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spread, depth, imbalance, roll_vol, ofi,
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sd_ratio, abs_imb, cum_ofi, roll_depth, ddepth
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])
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scaler = StandardScaler()
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X_scaled = scaler.fit_transform(X_full)
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return X_scaled, scaler
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# ─────────────────────────────────────────
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# 3. HMM Fitting
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# ─────────────────────────────────────────
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def fit_hmm(X, n_components=N_REGIMES, n_restarts=12, rng_seed=SEED):
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best_score, best_model = -np.inf, None
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for k in range(n_restarts):
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model = GaussianHMM(
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n_components = n_components,
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covariance_type = "full",
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n_iter = 400,
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tol = 1e-7,
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random_state = rng_seed + k,
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init_params = "stmc",
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params = "stmc",
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)
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try:
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model.fit(X)
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sc = model.score(X)
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if sc > best_score:
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best_score, best_model = sc, model
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except Exception:
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continue
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if best_model is None:
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raise RuntimeError("HMM fitting failed across all restarts.")
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return best_model
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# ─────────────────────────────────────────
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# 4. Stress Event Definition (UNCHANGED)
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# ─────────────────────────────────────────
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def define_stress_events(X_raw, fw=FW_WINDOW, pct=STRESS_PCT):
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spread = X_raw[:, 0]
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threshold = np.percentile(spread, pct)
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sigma = np.array([
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t for t in range(len(spread) - fw)
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if np.mean(spread[t+1:t+fw+1]) > threshold
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], dtype=int)
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return sigma
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# ─────────────────────────────────────────
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# 5. Posterior-Based Signal Computation
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# (same architecture as v3, unchanged)
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# ─────────────────────────────────────────
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def smooth_posterior(posterior, window=7):
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"""Causal trailing rolling mean — no look-ahead."""
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return pd.DataFrame(posterior).rolling(window, min_periods=1).mean().values
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def entropy_signal(post):
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eps = 1e-12
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return -np.sum(post * np.log(post + eps), axis=1)
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def uncertainty_signal(post):
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return 1.0 - post.max(axis=1)
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def transition_intensity_signal(post):
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ti = np.abs(np.diff(post, axis=0)).sum(axis=1)
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return np.concatenate([[0.0], ti])
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def prestress_posterior_signal(post, model):
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means_raw = model.means_[:, 0] # spread dimension
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state_rank = np.argsort(means_raw)
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prestress_id = state_rank[1] # intermediate spread state
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return post[:, prestress_id]
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def _norm01(x):
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lo, hi = x.min(), x.max()
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return (x - lo) / (hi - lo + 1e-12)
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def build_composite_score(post, model):
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H = entropy_signal(post)
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U = uncertainty_signal(post)
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TI = transition_intensity_signal(post)
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PS = prestress_posterior_signal(post, model)
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score = (W_ENTROPY * _norm01(H) +
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W_UNCERT * _norm01(U) +
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W_TRANS * _norm01(TI) +
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W_PRESTRESS * _norm01(PS))
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return score, H, U, TI, PS
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def deduplicate(indices, min_gap=MIN_GAP):
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if len(indices) == 0:
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return np.array([], dtype=int)
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out = [indices[0]]
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for idx in indices[1:]:
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if idx - out[-1] >= min_gap:
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out.append(idx)
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return np.array(out, dtype=int)
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def model_signals(model, X_scaled, smooth_win=7,
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signal_pct=SIGNAL_PCT, min_gap=MIN_GAP):
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posterior = model.predict_proba(X_scaled)
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post_smooth = smooth_posterior(posterior, window=smooth_win)
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score, H, U, TI, PS = build_composite_score(post_smooth, model)
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threshold = np.percentile(score, signal_pct)
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raw = np.where(score > threshold)[0]
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tau = deduplicate(raw, min_gap=min_gap)
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return tau, score, H, U, TI, PS
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def imbalance_baseline(X_raw, pct=90, min_gap=MIN_GAP):
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imb = np.abs(X_raw[:, 2])
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raw = np.where(imb > np.percentile(imb, pct))[0]
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return deduplicate(raw, min_gap=min_gap)
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def volatility_baseline(X_raw, pct=90, min_gap=MIN_GAP):
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rv = X_raw[:, 3]
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raw = np.where(rv > np.percentile(rv, pct))[0]
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return deduplicate(raw, min_gap=min_gap)
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# ─────────────────────────────────────────
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# 6. Lead-Time Evaluation (UNCHANGED)
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# ─────────────────────────────────────────
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def compute_lead_times(tau, sigma, max_lag=MAX_LAG):
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deltas = np.empty(len(tau), dtype=float)
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for i, t in enumerate(tau):
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cands = sigma[(sigma > t) & (sigma <= t + max_lag)]
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deltas[i] = (cands[0] - t) if len(cands) > 0 else PENALTY
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return deltas
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def evaluation_metrics(deltas):
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valid = deltas > 0
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return dict(
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mean_delta = float(np.mean(deltas)),
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pct_early = float(np.mean(valid)),
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mean_early = float(np.mean(deltas[valid])) if valid.any() else 0.0,
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std_delta = float(np.std(deltas)),
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n_tau = int(len(deltas)),
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n_early = int(valid.sum()),
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)
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# ─────────────────────────────────────────
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# 7. Bootstrap CI + Mann–Whitney (UNCHANGED)
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# ─────────────────────────────────────────
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def bootstrap_ci(deltas, stat_fn=np.mean, n_boot=N_BOOT, alpha=0.05, seed=SEED):
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rng = np.random.default_rng(seed)
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boot = np.array([
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stat_fn(rng.choice(deltas, size=len(deltas), replace=True))
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for _ in range(n_boot)
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])
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return (float(np.percentile(boot, 100*alpha/2)),
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float(np.percentile(boot, 100*(1-alpha/2))))
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def mannwhitney_test(a, b):
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return stats.mannwhitneyu(a, b, alternative="two-sided")
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# ─────────────────────────────────────────
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# 8. Visualisation
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# ─────────────────────────────────────────
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PALETTE = {
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"Model" : "#2C6FAC",
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"Imbalance" : "#D94F3D",
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"Volatility": "#5AAE61",
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}
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plt.rcParams.update({
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"font.family" : "serif",
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"font.size" : 11,
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"axes.spines.top" : False,
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"axes.spines.right": False,
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"axes.linewidth" : 0.8,
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"figure.dpi" : 150,
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})
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REGIME_FILL = {0: "#DDEEFF", 1: "#FFF3CD", 2: "#FFDDDD"}
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def plot_dgp_causal_structure(X_raw, Z_true, delay_map, n_show=2500):
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"""
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Three-panel overview of the causal DGP:
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1. Spread with true regime shading + Regime-1 onset arrows
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2. Depth
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3. Imbalance
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Arrows mark Regime-1 entry (τ_true); the mandatory delay to stress
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is annotated on the first few events.
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"""
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||
t_end = min(n_show, len(Z_true))
|
||
t_ax = np.arange(t_end)
|
||
spread = X_raw[:t_end, 0]
|
||
depth = X_raw[:t_end, 1]
|
||
imb = X_raw[:t_end, 2]
|
||
|
||
fig, axes = plt.subplots(3, 1, figsize=(13, 8), sharex=True)
|
||
fig.suptitle("Causal DGP: Hidden Build-Up (Regime 1) → Delayed Stress (Regime 2)",
|
||
fontsize=13, fontweight="bold")
|
||
|
||
for ax, y, ylabel in zip(axes,
|
||
[spread, depth, imb],
|
||
["Bid-Ask Spread", "Market Depth", "Order Imbalance"]):
|
||
for k, c in REGIME_FILL.items():
|
||
ax.fill_between(t_ax, y.min(), y.max(),
|
||
where=Z_true[:t_end] == k, color=c, alpha=0.55)
|
||
ax.plot(t_ax, y, lw=0.65, color="#1A1A2E")
|
||
ax.set_ylabel(ylabel)
|
||
|
||
# Annotate first 5 Regime-1 onsets with delay arrows on spread panel
|
||
ax0 = axes[0]
|
||
shown = 0
|
||
for t_entry, k in sorted(delay_map.items()):
|
||
if t_entry >= t_end:
|
||
break
|
||
t_stress = min(t_entry + k, t_end - 1)
|
||
y_ann = spread[t_entry] * 1.08
|
||
ax0.annotate(
|
||
"", xy=(t_stress, y_ann * 1.06), xytext=(t_entry, y_ann),
|
||
arrowprops=dict(arrowstyle="->", color="#CC6600", lw=1.3),
|
||
)
|
||
ax0.text(t_entry, y_ann * 1.02, f"k={k}", fontsize=7,
|
||
color="#CC6600", ha="left")
|
||
shown += 1
|
||
if shown >= 5:
|
||
break
|
||
|
||
# Custom legend
|
||
from matplotlib.patches import Patch
|
||
legend_elems = [Patch(fc=REGIME_FILL[k], label=f"Regime {k}") for k in range(3)]
|
||
axes[0].legend(handles=legend_elems, loc="upper right",
|
||
fontsize=8, frameon=False, ncol=3)
|
||
axes[2].set_xlabel("Timestep")
|
||
fig.tight_layout()
|
||
plt.savefig("lob_dgp_structure.pdf", bbox_inches="tight")
|
||
plt.show()
|
||
|
||
|
||
def plot_composite_signal(X_raw, Z_true, score, tau_model, sigma, n_show=3000):
|
||
"""Four-panel: spread + regimes, composite score + signals, depth, imbalance."""
|
||
t_end = min(n_show, len(Z_true))
|
||
t_ax = np.arange(t_end)
|
||
|
||
tau_vis = tau_model[tau_model < t_end]
|
||
sigma_vis = sigma[sigma < t_end]
|
||
sc = score[:t_end]
|
||
thresh = np.percentile(score, SIGNAL_PCT)
|
||
|
||
spread = X_raw[:t_end, 0]
|
||
depth = X_raw[:t_end, 1]
|
||
imb = X_raw[:t_end, 2]
|
||
|
||
fig, axes = plt.subplots(4, 1, figsize=(13, 10), sharex=True,
|
||
gridspec_kw={"height_ratios": [2, 2.5, 1.5, 1.5]})
|
||
fig.suptitle("Posterior-Based Instability Detector — v4 (Causal DGP)",
|
||
fontsize=13, fontweight="bold")
|
||
|
||
# Panel 1: spread + regime shading
|
||
ax = axes[0]
|
||
for k, c in REGIME_FILL.items():
|
||
ax.fill_between(t_ax, 0, spread.max()*1.1,
|
||
where=Z_true[:t_end] == k, color=c, alpha=0.55,
|
||
label=f"Regime {k}")
|
||
ax.plot(t_ax, spread, lw=0.65, color="#1A1A2E")
|
||
ax.set_ylabel("Spread")
|
||
ax.legend(loc="upper right", fontsize=8, frameon=False, ncol=3)
|
||
|
||
# Panel 2: composite score + signals
|
||
ax = axes[1]
|
||
ax.plot(t_ax, sc, lw=0.8, color="#444444", alpha=0.85, label="Composite score")
|
||
ax.axhline(thresh, color="#FF8800", lw=1.2, ls="--",
|
||
label=f"{SIGNAL_PCT}th pct threshold")
|
||
ax.fill_between(t_ax, thresh, sc, where=sc > thresh,
|
||
color=PALETTE["Model"], alpha=0.18)
|
||
ax.vlines(tau_vis, sc.min(), sc.max(),
|
||
color=PALETTE["Model"], lw=1.0, alpha=0.75, label="Signal τ (model)")
|
||
ax.vlines(sigma_vis, sc.min(), sc.max(),
|
||
color=PALETTE["Imbalance"], lw=0.6, ls=":", alpha=0.45,
|
||
label="Stress event σ")
|
||
ax.set_ylabel("Instability Score")
|
||
ax.legend(loc="upper right", fontsize=8, frameon=False, ncol=2)
|
||
|
||
# Panel 3: depth
|
||
ax = axes[2]
|
||
ax.plot(t_ax, depth, lw=0.7, color="#2D6A4F")
|
||
ax.set_ylabel("Depth")
|
||
|
||
# Panel 4: imbalance
|
||
ax = axes[3]
|
||
ax.plot(t_ax, imb, lw=0.7, color="#6A3D9A", alpha=0.85)
|
||
ax.set_ylabel("Imbalance")
|
||
ax.set_xlabel("Timestep")
|
||
|
||
fig.tight_layout()
|
||
plt.savefig("lob_composite_signal.pdf", bbox_inches="tight")
|
||
plt.show()
|
||
|
||
|
||
def plot_lead_time_densities(delta_dict, max_lag=MAX_LAG):
|
||
fig, ax = plt.subplots(figsize=(9, 5))
|
||
x_grid = np.linspace(-max_lag - 5, max_lag + 5, 800)
|
||
|
||
for i, (name, deltas) in enumerate(delta_dict.items()):
|
||
color = PALETTE[name]
|
||
valid = deltas[deltas > PENALTY]
|
||
if len(valid) > 5:
|
||
kde = gaussian_kde(valid, bw_method="scott")
|
||
ax.plot(x_grid, kde(x_grid), lw=2.4, color=color, label=name)
|
||
ax.fill_between(x_grid, kde(x_grid), alpha=0.14, color=color)
|
||
missed = np.mean(deltas <= PENALTY)
|
||
mean_v = np.mean(deltas[deltas > 0]) if (deltas > 0).any() else 0
|
||
ax.annotate(
|
||
f"{name} missed={missed:.1%} E[Δ|early]={mean_v:+.1f}",
|
||
xy=(-max_lag + 1, 0.007 * (i + 1)),
|
||
color=color, fontsize=8.5, fontweight="bold"
|
||
)
|
||
|
||
ax.axvline(0, color="gray", lw=1.2, ls="--", label="Zero lead-time")
|
||
ax.set_xlabel("Lead time Δ (timesteps before stress)", labelpad=8)
|
||
ax.set_ylabel("Density", labelpad=8)
|
||
ax.set_title("Lead-Time Distribution: Posterior-Based Model vs Baselines [v4]",
|
||
fontsize=13, pad=10)
|
||
ax.legend(frameon=False, fontsize=10)
|
||
ax.set_xlim(-max_lag - 2, max_lag + 2)
|
||
fig.tight_layout()
|
||
plt.savefig("lob_lead_time.pdf", bbox_inches="tight")
|
||
plt.show()
|
||
|
||
|
||
def plot_results_table(results_df):
|
||
fig, ax = plt.subplots(figsize=(14, 2.4))
|
||
ax.axis("off")
|
||
tbl = ax.table(cellText=results_df.values, colLabels=results_df.columns,
|
||
cellLoc="center", loc="center")
|
||
tbl.auto_set_font_size(False)
|
||
tbl.set_fontsize(9.5)
|
||
tbl.scale(1.2, 1.7)
|
||
for j in range(len(results_df.columns)):
|
||
tbl[0, j].set_facecolor("#2C6FAC")
|
||
tbl[0, j].set_text_props(color="white", fontweight="bold")
|
||
for j in range(len(results_df.columns)):
|
||
tbl[1, j].set_facecolor("#EDF4FF")
|
||
fig.suptitle(
|
||
"Detection Performance Summary — v4 (Causal DGP + Posterior-Based Signals)",
|
||
fontsize=10, y=1.02)
|
||
fig.tight_layout()
|
||
plt.savefig("lob_results_table.pdf", bbox_inches="tight")
|
||
plt.show()
|
||
|
||
|
||
def plot_delay_distribution(delay_map, T):
|
||
"""Histogram of true Regime-1 delays (ground truth from DGP)."""
|
||
delays = list(delay_map.values())
|
||
fig, ax = plt.subplots(figsize=(7, 3.5))
|
||
ax.hist(delays, bins=20, color=PALETTE["Model"], alpha=0.75, edgecolor="white")
|
||
ax.axvline(np.mean(delays), color="#FF8800", lw=1.5, ls="--",
|
||
label=f"Mean delay = {np.mean(delays):.1f} steps")
|
||
ax.set_xlabel("True delay k (Regime-1 → Regime-2, steps)")
|
||
ax.set_ylabel("Count")
|
||
ax.set_title("Ground-Truth Delay Distribution (DGP)")
|
||
ax.legend(frameon=False)
|
||
fig.tight_layout()
|
||
plt.savefig("lob_delay_dist.pdf", bbox_inches="tight")
|
||
plt.show()
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 9. Sanity Check: Verify Baselines Are Blind to Regime 1
|
||
# ─────────────────────────────────────────
|
||
|
||
def check_baseline_blindness(X_raw, Z_true):
|
||
"""
|
||
Prints percentile statistics of imbalance and rolling-vol
|
||
in each regime, confirming that Regime-1 values do NOT
|
||
exceed the 90th-percentile thresholds used by the baselines.
|
||
"""
|
||
imb = np.abs(X_raw[:, 2])
|
||
roll_vol = X_raw[:, 3]
|
||
imb_thr = np.percentile(imb, 90)
|
||
vol_thr = np.percentile(roll_vol, 90)
|
||
|
||
print(" ── Baseline Blindness Sanity Check ──────────────────────")
|
||
print(f" Imbalance 90th-pct threshold : {imb_thr:.4f}")
|
||
print(f" Volatility 90th-pct threshold : {vol_thr:.4f}")
|
||
for k in range(3):
|
||
mask = Z_true == k
|
||
print(f" Regime {k} | "
|
||
f"mean |imb| = {imb[mask].mean():.4f} "
|
||
f"(frac > thr: {(imb[mask] > imb_thr).mean():.2%}) | "
|
||
f"mean rv = {roll_vol[mask].mean():.4f} "
|
||
f"(frac > thr: {(roll_vol[mask] > vol_thr).mean():.2%})")
|
||
print(" → Regime 1 should have low 'frac > thr' for both metrics")
|
||
print()
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 10. Main Pipeline
|
||
# ─────────────────────────────────────────
|
||
|
||
def run_experiment():
|
||
rng = np.random.default_rng(SEED)
|
||
|
||
print("=" * 68)
|
||
print(" LOB Micro-Regime Detection v4")
|
||
print(" Causal Delayed Stress DGP + Posterior Instability Signals")
|
||
print("=" * 68)
|
||
|
||
# ── Step 1: Data generation ──────────────────────────────────────
|
||
print("\n Step 1 / 6 — Generating causal LOB data …")
|
||
X_raw, Z_true, delay_map = generate_lob_data(T, rng)
|
||
regime_dist = " | ".join(
|
||
[f"Regime {k}: {(Z_true==k).mean():.1%}" for k in range(N_REGIMES)])
|
||
print(f" {T:,} timesteps | {regime_dist}")
|
||
print(f" Regime-1 episodes: {len(delay_map)} "
|
||
f"| Mean delay to stress: {np.mean(list(delay_map.values())):.1f} steps")
|
||
|
||
# ── Step 2: Feature engineering ──────────────────────────────────
|
||
print("\n Step 2 / 6 — Feature engineering …")
|
||
X_scaled, scaler = engineer_features(X_raw)
|
||
print(f" Feature matrix: {X_scaled.shape}")
|
||
|
||
# ── Step 3: HMM ──────────────────────────────────────────────────
|
||
print("\n Step 3 / 6 — Fitting HMM (12 restarts) …")
|
||
model = fit_hmm(X_scaled)
|
||
Z_hat = model.predict(X_scaled)
|
||
ll = model.score(X_scaled)
|
||
conv = model.monitor_.converged
|
||
print(f" Best log-likelihood: {ll:,.2f} | Converged: {conv}")
|
||
means_sp = model.means_[:, 0]
|
||
state_rank = np.argsort(means_sp)
|
||
print(f" HMM state ranking by spread: {state_rank.tolist()} (low → high)")
|
||
|
||
# ── Step 4: Stress events ─────────────────────────────────────────
|
||
print("\n Step 4 / 6 — Stress event definition …")
|
||
sigma = define_stress_events(X_raw)
|
||
print(f" Stress events: {len(sigma):,} ({len(sigma)/T:.1%} of timesteps)")
|
||
|
||
# ── Step 4b: Sanity check ─────────────────────────────────────────
|
||
print()
|
||
check_baseline_blindness(X_raw, Z_true)
|
||
|
||
# ── Step 5: Signals ───────────────────────────────────────────────
|
||
print(" Step 5 / 6 — Computing signals …")
|
||
tau_model, score, H, U, TI, PS = model_signals(model, X_scaled)
|
||
tau_imb = imbalance_baseline(X_raw)
|
||
tau_vol = volatility_baseline(X_raw)
|
||
print(f" Signals — Model: {len(tau_model)} | "
|
||
f"Imbalance: {len(tau_imb)} | Volatility: {len(tau_vol)}")
|
||
|
||
delta_model = compute_lead_times(tau_model, sigma)
|
||
delta_imb = compute_lead_times(tau_imb, sigma)
|
||
delta_vol = compute_lead_times(tau_vol, sigma)
|
||
delta_dict = {"Model": delta_model,
|
||
"Imbalance": delta_imb,
|
||
"Volatility": delta_vol}
|
||
|
||
# ── Step 6: Statistical validation ───────────────────────────────
|
||
print("\n Step 6 / 6 — Statistical validation …")
|
||
rows = []
|
||
for name, deltas in delta_dict.items():
|
||
m = evaluation_metrics(deltas)
|
||
lo, hi = bootstrap_ci(deltas)
|
||
rows.append({
|
||
"Detector" : name,
|
||
"Mean Δ" : f"{m['mean_delta']:+.2f}",
|
||
"95% CI" : f"[{lo:+.2f}, {hi:+.2f}]",
|
||
"% Early" : f"{m['pct_early']:.1%}",
|
||
"Mean Δ | early" : f"{m['mean_early']:+.2f}",
|
||
"Std Δ" : f"{m['std_delta']:.2f}",
|
||
"N(τ)" : m['n_tau'],
|
||
"N(early)" : m['n_early'],
|
||
})
|
||
|
||
results_df = pd.DataFrame(rows)
|
||
print("\n" + results_df.to_string(index=False))
|
||
|
||
print("\n Pairwise Mann–Whitney U tests (two-sided):")
|
||
pairs = [("Model", "Imbalance"),
|
||
("Model", "Volatility"),
|
||
("Imbalance", "Volatility")]
|
||
for a, b in pairs:
|
||
u, p = mannwhitney_test(delta_dict[a], delta_dict[b])
|
||
sig = ("***" if p < 0.001 else
|
||
"**" if p < 0.01 else
|
||
"*" if p < 0.05 else "ns")
|
||
print(f" {a:12s} vs {b:12s}: U={u:,.0f} p={p:.4f} {sig}")
|
||
|
||
# ── Figures ───────────────────────────────────────────────────────
|
||
print("\n Rendering figures …")
|
||
plot_dgp_causal_structure(X_raw, Z_true, delay_map)
|
||
plot_delay_distribution(delay_map, T)
|
||
plot_composite_signal(X_raw, Z_true, score, tau_model, sigma)
|
||
plot_lead_time_densities(delta_dict)
|
||
plot_results_table(results_df)
|
||
|
||
print("\n Experiment complete.")
|
||
return (results_df, delta_dict, model,
|
||
X_raw, Z_true, Z_hat, sigma, delay_map,
|
||
score, H, U, TI)
|
||
|
||
|
||
if __name__ == "__main__":
|
||
(results_df, delta_dict, model,
|
||
X_raw, Z_true, Z_hat, sigma, delay_map,
|
||
score, H, U, TI) = run_experiment()
|