1020 lines
40 KiB
Python
1020 lines
40 KiB
Python
# ============================================================
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# Latent Micro-Regimes in Limit Order Books:
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# Identification and Early Detection — v5
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# ─────────────────────────────────────────
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# KEY UPGRADE: Hybrid Instability Signal
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#
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# The core detection failure in v4 was that entropy alone
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# detects STATE TRANSITIONS, not PRE-TRANSITION DRIFT.
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# Regime 1 is gradual, weak, and multi-dimensional — no single
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# HMM posterior channel can integrate the subtle build-up.
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#
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# v5 Fix: Hybrid signal S_t combining:
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# 1. HMM posterior entropy (probabilistic channel)
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# 2. Drift in spread (temporal drift channel)
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# 3. Depth deterioration (structural erosion channel)
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# 4. Pre-stress posterior (HMM Regime-1 fingerprint)
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# 5. Cumulative OFI drift (order-flow momentum)
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#
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# Each channel is normalized [0,1], then fused via
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# interpretable weights. Threshold is adaptive (percentile).
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# Result: early detection BEFORE regime switch, not after.
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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
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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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# ── Hybrid signal weights ─────────────────────────────────────
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# These are the five channels of the hybrid instability score.
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# Drift channels (w_drift_sp, w_depth_det, w_ofi_mom) are the
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# NEW additions that capture the Regime-1 build-up signature.
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W_ENTROPY = 0.25 # HMM posterior entropy
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W_PRESTRESS = 0.20 # HMM Regime-1 posterior probability
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W_DRIFT_SP = 0.25 # temporal drift: spread rising trend
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W_DEPTH_DET = 0.20 # structural erosion: depth dropping
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W_OFI_MOM = 0.10 # cumulative order-flow imbalance momentum
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# Detection threshold percentile (adaptive)
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SIGNAL_PCT = 88
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# DGP delay parameters (unchanged)
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DELAY_LO = 10
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DELAY_HI = 50
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BLEND_WIN = 8
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np.random.seed(SEED)
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# ─────────────────────────────────────────
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# 1. Causal Delayed Stress DGP (UNCHANGED)
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# ─────────────────────────────────────────
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REGIME_PARAMS = {
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0: dict(
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sp_mu=1.5, sp_sig=0.20,
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dp_ar=0.95, dp_mu=120.0, dp_sig=6.0,
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ib_mu=0.00, ib_sig=0.06,
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vol_noise=0.02,
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),
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1: dict(
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sp_mu=2.4, sp_sig=0.35,
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dp_ar=0.93, dp_mu=92.0, dp_sig=9.0,
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ib_mu=0.12, ib_sig=0.09,
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vol_noise=0.06,
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),
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2: dict(
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sp_mu=8.0, sp_sig=1.30,
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dp_ar=0.88, dp_mu=35.0, dp_sig=18.0,
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ib_mu=0.50, ib_sig=0.20,
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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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return int(rng.integers(DELAY_LO, DELAY_HI + 1))
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def _draw_crisis_duration(rng):
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return int(rng.integers(15, 61))
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def _draw_stable_duration(rng):
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return int(rng.integers(80, 301))
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def build_regime_sequence(T, rng):
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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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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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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
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t = end1
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if t >= T:
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break
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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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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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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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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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if spread[t] > np.exp(base + 0.8 * p['sp_sig']):
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hawkes += 0.30
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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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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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spread = _blend(spread, Z)
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depth = _blend(depth, Z)
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imbalance = _blend(imbalance, Z)
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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 (UNCHANGED)
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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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ddepth = -pd.Series(depth).diff(5).fillna(0).values
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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 (UNCHANGED)
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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. HYBRID INSTABILITY SIGNAL ← CORE UPGRADE
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# ─────────────────────────────────────────
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#
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# Architecture:
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# ┌─────────────────────────────────────────────────────────┐
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# │ Channel 1: HMM Entropy — captures uncertainty │
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# │ Channel 2: HMM Pre-stress — Regime-1 fingerprint │
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# │ Channel 3: Spread drift — temporal momentum │
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# │ Channel 4: Depth erosion — structural deterioration│
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# │ Channel 5: OFI momentum — order-flow pressure │
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# └─────────────────────────────────────────────────────────┘
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#
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# All channels are:
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# (a) computed causally (trailing windows only)
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# (b) normalized to [0,1]
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# (c) fused via interpretable linear weights
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#
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# The KEY insight: channels 3-5 are TEMPORAL DRIFT features
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# that accumulate during Regime 1 before any regime switch
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# is detectable by the HMM alone.
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# ─────────────────────────────────────────
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def _norm01(x):
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"""Min-max normalize to [0,1]."""
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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 _causal_rolling(series, window, fn='mean'):
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"""Strictly causal rolling statistic (trailing window)."""
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s = pd.Series(series)
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if fn == 'mean':
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return s.rolling(window, min_periods=1).mean().values
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elif fn == 'std':
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return s.rolling(window, min_periods=1).std().fillna(0).values
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elif fn == 'sum':
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return s.rolling(window, min_periods=1).sum().values
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# ── Channel 1 & 2: HMM posterior channels ──────────────────────
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def hmm_entropy_signal(post):
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"""Shannon entropy of posterior — high near transitions."""
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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 hmm_prestress_signal(post, model):
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"""
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Posterior probability of the intermediate-spread HMM state.
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This state corresponds to Regime 1 (build-up) in the DGP.
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We identify it as the state with median mean spread.
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"""
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means_raw = model.means_[:, 0] # spread dimension (feature 0)
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state_rank = np.argsort(means_raw)
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prestress_id = state_rank[1] # median spread = pre-stress state
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return post[:, prestress_id]
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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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# ── Channel 3: Spread temporal drift ────────────────────────────
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def spread_drift_signal(spread, short_win=10, long_win=40):
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"""
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Detect upward drift in spread BEFORE it becomes a spike.
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Method: difference of rolling means (fast MA - slow MA).
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Positive values = spread is rising faster than its recent average.
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This captures the gradual Regime-1 spread elevation.
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We also include the rolling slope (linear trend over short window)
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and combine them for robustness.
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"""
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s = pd.Series(spread)
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# Fast vs slow MA crossover (positive = rising trend)
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fast_ma = s.rolling(short_win, min_periods=1).mean()
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slow_ma = s.rolling(long_win, min_periods=1).mean()
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ma_cross = (fast_ma - slow_ma).values
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ma_cross = np.clip(ma_cross, 0, None) # only rising trend matters
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# Rolling first differences (momentum)
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d_spread = s.diff(1).fillna(0)
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spread_mom = d_spread.rolling(short_win, min_periods=1).mean().values
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spread_mom = np.clip(spread_mom, 0, None) # only upward momentum
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# Cumulative drift: rolling sum of positive increments
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cum_drift = d_spread.clip(lower=0).rolling(long_win, min_periods=1).sum().values
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# Combine: all three sub-channels capture build-up from different angles
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drift = (_norm01(ma_cross) +
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_norm01(spread_mom) +
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_norm01(cum_drift)) / 3.0
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return drift
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# ── Channel 4: Depth deterioration ──────────────────────────────
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def depth_erosion_signal(depth, win_short=10, win_long=50):
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"""
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Detect gradual depth erosion — the AR-decay signature of Regime 1.
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Method: negative of depth trend (depth falling = erosion rising).
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We use both level and velocity (rate of change) to be sensitive
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to the slow AR-decay in Regime 1, not just the Regime-2 collapse.
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"""
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d = pd.Series(depth)
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# Rolling mean depth (trend)
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depth_trend = d.rolling(win_short, min_periods=1).mean().values
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# Depth velocity: how fast is depth falling? (negative diff = erosion)
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d_depth = -d.diff(5).fillna(0).values # positive = erosion
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depth_vel = _causal_rolling(d_depth, win_short, fn='mean')
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depth_vel = np.clip(depth_vel, 0, None)
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# Depth vs long-run baseline: how far below the rolling 50-step mean?
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depth_long = d.rolling(win_long, min_periods=1).mean().values
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depth_below_baseline = np.clip(depth_long - depth_trend, 0, None)
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erosion = (_norm01(depth_vel) +
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_norm01(depth_below_baseline)) / 2.0
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return erosion
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# ── Channel 5: OFI cumulative momentum ──────────────────────────
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def ofi_momentum_signal(imbalance, ofi, win=30):
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"""
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Cumulative directional pressure from order-flow imbalance.
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Regime 1 has ib_mu=0.12 (mild directional bias) vs 0.00 in Regime 0.
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This channel tracks whether imbalance has been systematically biased
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over a rolling window — the OFI momentum.
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"""
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# Rolling mean of absolute imbalance (directional pressure)
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abs_imb = np.abs(imbalance)
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mom_imb = _causal_rolling(abs_imb, win, fn='mean')
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# Rolling mean of OFI magnitude
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abs_ofi = np.abs(ofi)
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mom_ofi = _causal_rolling(abs_ofi, win, fn='mean')
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momentum = (_norm01(mom_imb) + _norm01(mom_ofi)) / 2.0
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return momentum
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# ── Hybrid fusion ────────────────────────────────────────────────
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def build_hybrid_score(post_smooth, model, X_raw):
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"""
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Fuse HMM posterior channels with temporal drift channels
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into a single instability score S_t.
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S_t = w1*entropy + w2*prestress + w3*drift_spread
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+ w4*depth_erosion + w5*ofi_momentum
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Parameters
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----------
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post_smooth : (T, n_states) smoothed HMM posterior
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model : fitted GaussianHMM
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X_raw : (T, 5) raw feature matrix
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Returns
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-------
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score : (T,) hybrid instability score
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comps : dict of individual normalized channels (for diagnostics)
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"""
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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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ofi = X_raw[:, 4]
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# ── Probabilistic channels ────────────────────────────────────
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entropy = hmm_entropy_signal(post_smooth)
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prestress = hmm_prestress_signal(post_smooth, model)
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c_entropy = _norm01(entropy)
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c_prestress = _norm01(prestress)
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# ── Temporal drift channels ───────────────────────────────────
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c_drift_sp = _norm01(spread_drift_signal(spread))
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c_depth_det = _norm01(depth_erosion_signal(depth))
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c_ofi_mom = _norm01(ofi_momentum_signal(imbalance, ofi))
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# ── Weighted fusion ───────────────────────────────────────────
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score = (W_ENTROPY * c_entropy +
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W_PRESTRESS * c_prestress +
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W_DRIFT_SP * c_drift_sp +
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W_DEPTH_DET * c_depth_det +
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W_OFI_MOM * c_ofi_mom)
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comps = {
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'entropy' : c_entropy,
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'prestress' : c_prestress,
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'drift_spread': c_drift_sp,
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'depth_erosion': c_depth_det,
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'ofi_momentum': c_ofi_mom,
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}
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return score, comps
|
||
|
||
|
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def deduplicate(indices, min_gap=MIN_GAP):
|
||
if len(indices) == 0:
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return np.array([], dtype=int)
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||
out = [indices[0]]
|
||
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, X_raw,
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smooth_win=7, signal_pct=SIGNAL_PCT, min_gap=MIN_GAP):
|
||
"""
|
||
Full pipeline: posterior → smooth → hybrid score → threshold → signals.
|
||
"""
|
||
posterior = model.predict_proba(X_scaled)
|
||
post_smooth = smooth_posterior(posterior, window=smooth_win)
|
||
|
||
score, comps = build_hybrid_score(post_smooth, model, X_raw)
|
||
|
||
threshold = np.percentile(score, signal_pct)
|
||
raw = np.where(score > threshold)[0]
|
||
tau = deduplicate(raw, min_gap=min_gap)
|
||
|
||
return tau, score, comps, post_smooth
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 6. Baselines (UNCHANGED)
|
||
# ─────────────────────────────────────────
|
||
|
||
def imbalance_baseline(X_raw, pct=90, min_gap=MIN_GAP):
|
||
imb = np.abs(X_raw[:, 2])
|
||
raw = np.where(imb > np.percentile(imb, pct))[0]
|
||
return deduplicate(raw, min_gap=min_gap)
|
||
|
||
|
||
def volatility_baseline(X_raw, pct=90, min_gap=MIN_GAP):
|
||
rv = X_raw[:, 3]
|
||
raw = np.where(rv > np.percentile(rv, pct))[0]
|
||
return deduplicate(raw, min_gap=min_gap)
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 7. Lead-Time Evaluation (UNCHANGED)
|
||
# ─────────────────────────────────────────
|
||
|
||
def compute_lead_times(tau, sigma, max_lag=MAX_LAG):
|
||
deltas = np.empty(len(tau), dtype=float)
|
||
for i, t in enumerate(tau):
|
||
cands = sigma[(sigma > t) & (sigma <= t + max_lag)]
|
||
deltas[i] = (cands[0] - t) if len(cands) > 0 else PENALTY
|
||
return deltas
|
||
|
||
|
||
def evaluation_metrics(deltas):
|
||
valid = deltas > 0
|
||
return dict(
|
||
mean_delta = float(np.mean(deltas)),
|
||
pct_early = float(np.mean(valid)),
|
||
mean_early = float(np.mean(deltas[valid])) if valid.any() else 0.0,
|
||
std_delta = float(np.std(deltas)),
|
||
n_tau = int(len(deltas)),
|
||
n_early = int(valid.sum()),
|
||
)
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 8. Bootstrap CI + Mann–Whitney (UNCHANGED)
|
||
# ─────────────────────────────────────────
|
||
|
||
def bootstrap_ci(deltas, stat_fn=np.mean, n_boot=N_BOOT, alpha=0.05, seed=SEED):
|
||
rng = np.random.default_rng(seed)
|
||
boot = np.array([
|
||
stat_fn(rng.choice(deltas, size=len(deltas), replace=True))
|
||
for _ in range(n_boot)
|
||
])
|
||
return (float(np.percentile(boot, 100*alpha/2)),
|
||
float(np.percentile(boot, 100*(1-alpha/2))))
|
||
|
||
|
||
def mannwhitney_test(a, b):
|
||
return stats.mannwhitneyu(a, b, alternative="two-sided")
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 9. Visualisation
|
||
# ─────────────────────────────────────────
|
||
|
||
PALETTE = {
|
||
"Model" : "#2C6FAC",
|
||
"Imbalance" : "#D94F3D",
|
||
"Volatility": "#5AAE61",
|
||
}
|
||
|
||
plt.rcParams.update({
|
||
"font.family" : "serif",
|
||
"font.size" : 11,
|
||
"axes.spines.top" : False,
|
||
"axes.spines.right": False,
|
||
"axes.linewidth" : 0.8,
|
||
"figure.dpi" : 150,
|
||
})
|
||
|
||
REGIME_FILL = {0: "#DDEEFF", 1: "#FFF3CD", 2: "#FFDDDD"}
|
||
|
||
|
||
def plot_dgp_causal_structure(X_raw, Z_true, delay_map, n_show=2500):
|
||
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)
|
||
|
||
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
|
||
|
||
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_hybrid_signal_decomposition(X_raw, Z_true, score, comps,
|
||
tau_model, sigma, n_show=3000):
|
||
"""
|
||
NEW in v5: Six-panel decomposition of the hybrid signal.
|
||
Shows each channel and the fused score with detections.
|
||
"""
|
||
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)
|
||
|
||
channel_labels = {
|
||
'entropy' : f"HMM Entropy (w={W_ENTROPY})",
|
||
'prestress' : f"HMM Pre-Stress (w={W_PRESTRESS})",
|
||
'drift_spread' : f"Spread Drift (w={W_DRIFT_SP})",
|
||
'depth_erosion': f"Depth Erosion (w={W_DEPTH_DET})",
|
||
'ofi_momentum' : f"OFI Momentum (w={W_OFI_MOM})",
|
||
}
|
||
channel_colors = {
|
||
'entropy' : "#555588",
|
||
'prestress' : "#AA5522",
|
||
'drift_spread' : "#228844",
|
||
'depth_erosion': "#882244",
|
||
'ofi_momentum' : "#224488",
|
||
}
|
||
|
||
fig, axes = plt.subplots(7, 1, figsize=(14, 16), sharex=True,
|
||
gridspec_kw={"height_ratios": [1.8, 1, 1, 1, 1, 1, 2]})
|
||
fig.suptitle("Hybrid Instability Signal Decomposition — v5",
|
||
fontsize=13, fontweight="bold")
|
||
|
||
# Spread + regime shading
|
||
ax = axes[0]
|
||
spread = X_raw[:t_end, 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)
|
||
|
||
# Individual channels
|
||
for i, (key, label) in enumerate(channel_labels.items()):
|
||
ax = axes[i + 1]
|
||
ch = comps[key][:t_end]
|
||
ax.plot(t_ax, ch, lw=0.75, color=channel_colors[key], alpha=0.9)
|
||
ax.fill_between(t_ax, 0, ch, alpha=0.12, color=channel_colors[key])
|
||
# Shade Regime-1 periods to show alignment
|
||
ax.fill_between(t_ax, 0, ch.max(),
|
||
where=Z_true[:t_end] == 1,
|
||
color=REGIME_FILL[1], alpha=0.30, zorder=0)
|
||
ax.set_ylabel(label, fontsize=8)
|
||
ax.set_ylim(0, 1.05)
|
||
|
||
# Fused hybrid score
|
||
ax = axes[6]
|
||
ax.plot(t_ax, sc, lw=0.9, color="#222222", alpha=0.85, label="Hybrid score")
|
||
ax.axhline(thresh, color="#FF8800", lw=1.2, ls="--",
|
||
label=f"{SIGNAL_PCT}th pct")
|
||
ax.fill_between(t_ax, thresh, sc, where=sc > thresh,
|
||
color=PALETTE["Model"], alpha=0.25)
|
||
ax.vlines(tau_vis, 0, sc.max(),
|
||
color=PALETTE["Model"], lw=1.0, alpha=0.8, label="Signal τ")
|
||
ax.vlines(sigma_vis, 0, sc.max(),
|
||
color=PALETTE["Imbalance"], lw=0.6, ls=":", alpha=0.4,
|
||
label="Stress σ")
|
||
ax.set_ylabel("Hybrid Score")
|
||
ax.set_xlabel("Timestep")
|
||
ax.legend(loc="upper right", fontsize=8, frameon=False, ncol=2)
|
||
|
||
fig.tight_layout()
|
||
plt.savefig("lob_hybrid_decomposition.pdf", bbox_inches="tight")
|
||
plt.show()
|
||
|
||
|
||
def plot_composite_signal(X_raw, Z_true, score, tau_model, sigma, n_show=3000):
|
||
"""Overview: spread, hybrid score, 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("Hybrid Posterior-Drift Instability Detector — v5 (Causal DGP)",
|
||
fontsize=13, fontweight="bold")
|
||
|
||
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)
|
||
|
||
ax = axes[1]
|
||
ax.plot(t_ax, sc, lw=0.8, color="#444444", alpha=0.85, label="Hybrid 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)
|
||
|
||
axes[2].plot(t_ax, depth, lw=0.7, color="#2D6A4F")
|
||
axes[2].set_ylabel("Depth")
|
||
|
||
axes[3].plot(t_ax, imb, lw=0.7, color="#6A3D9A", alpha=0.85)
|
||
axes[3].set_ylabel("Imbalance")
|
||
axes[3].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: Hybrid Model vs Baselines [v5]",
|
||
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 — v5 (Hybrid Posterior-Drift Signal)",
|
||
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):
|
||
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()
|
||
|
||
|
||
def plot_channel_importance(comps, Z_true, n_show=None):
|
||
"""
|
||
NEW in v5: Box plots comparing each channel's distribution
|
||
across regimes — shows which channels differentiate Regime 1.
|
||
"""
|
||
T_plot = n_show or len(Z_true)
|
||
fig, axes = plt.subplots(1, 5, figsize=(14, 4))
|
||
fig.suptitle("Channel Distributions by Regime — v5\n"
|
||
"(Regime 1 should be elevated vs Regime 0 for drift channels)",
|
||
fontsize=11)
|
||
|
||
channel_colors = {
|
||
'entropy' : "#555588",
|
||
'prestress' : "#AA5522",
|
||
'drift_spread' : "#228844",
|
||
'depth_erosion': "#882244",
|
||
'ofi_momentum' : "#224488",
|
||
}
|
||
regime_labels = {0: "Stable", 1: "Build-up", 2: "Crisis"}
|
||
|
||
for ax, (key, label) in zip(axes, {
|
||
'entropy' : "Entropy",
|
||
'prestress' : "Pre-Stress",
|
||
'drift_spread' : "Spread\nDrift",
|
||
'depth_erosion': "Depth\nErosion",
|
||
'ofi_momentum' : "OFI\nMomentum",
|
||
}.items()):
|
||
data = [comps[key][:T_plot][Z_true[:T_plot] == k] for k in range(3)]
|
||
bp = ax.boxplot(data, labels=[regime_labels[k] for k in range(3)],
|
||
patch_artist=True, notch=False, showfliers=False)
|
||
for patch, c in zip(bp['boxes'],
|
||
[REGIME_FILL[0], REGIME_FILL[1], REGIME_FILL[2]]):
|
||
patch.set_facecolor(c)
|
||
patch.set_edgecolor(channel_colors[key])
|
||
ax.set_title(label, fontsize=10, color=channel_colors[key])
|
||
ax.set_ylim(0, 1.05)
|
||
|
||
fig.tight_layout()
|
||
plt.savefig("lob_channel_importance.pdf", bbox_inches="tight")
|
||
plt.show()
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 10. Sanity Check (UNCHANGED)
|
||
# ─────────────────────────────────────────
|
||
|
||
def check_baseline_blindness(X_raw, Z_true):
|
||
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()
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 11. Main Pipeline
|
||
# ─────────────────────────────────────────
|
||
|
||
def run_experiment():
|
||
rng = np.random.default_rng(SEED)
|
||
|
||
print("=" * 68)
|
||
print(" LOB Micro-Regime Detection v5")
|
||
print(" Hybrid Posterior-Drift Signal (Temporal + Probabilistic)")
|
||
print("=" * 68)
|
||
|
||
# ── Step 1: Data generation ──────────────────────────────────────
|
||
print("\n Step 1 / 6 — Generating causal LOB data …")
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||
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)")
|
||
print(f"\n Signal weights:")
|
||
print(f" Entropy : {W_ENTROPY}")
|
||
print(f" Pre-Stress : {W_PRESTRESS}")
|
||
print(f" Spread Drift: {W_DRIFT_SP} ← NEW temporal drift")
|
||
print(f" Depth Erosion: {W_DEPTH_DET} ← NEW structural erosion")
|
||
print(f" OFI Momentum: {W_OFI_MOM} ← NEW order-flow momentum")
|
||
|
||
# ── 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: Hybrid signals ────────────────────────────────────────
|
||
print(" Step 5 / 6 — Computing hybrid signals …")
|
||
tau_model, score, comps, post_smooth = model_signals(
|
||
model, X_scaled, X_raw,
|
||
smooth_win=7, signal_pct=SIGNAL_PCT, min_gap=MIN_GAP
|
||
)
|
||
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}")
|
||
|
||
# ── Model mean Δ summary ──────────────────────────────────────────
|
||
m_model = evaluation_metrics(delta_model)
|
||
print(f"\n ── SUMMARY ──────────────────────────────────────")
|
||
print(f" Model Mean Δ : {m_model['mean_delta']:+.2f} steps")
|
||
print(f" Model % Early : {m_model['pct_early']:.1%}")
|
||
print(f" Model Mean Δ|early: {m_model['mean_early']:+.2f} steps")
|
||
if m_model['mean_delta'] > 0:
|
||
print(" ✓ Positive mean lead-time achieved")
|
||
if m_model['pct_early'] > 0.60:
|
||
print(" ✓ > 60% early detection rate achieved")
|
||
print()
|
||
|
||
# ── Figures ───────────────────────────────────────────────────────
|
||
print(" Rendering figures …")
|
||
plot_dgp_causal_structure(X_raw, Z_true, delay_map)
|
||
plot_delay_distribution(delay_map, T)
|
||
plot_hybrid_signal_decomposition(X_raw, Z_true, score, comps, tau_model, sigma)
|
||
plot_composite_signal(X_raw, Z_true, score, tau_model, sigma)
|
||
plot_lead_time_densities(delta_dict)
|
||
plot_channel_importance(comps, Z_true)
|
||
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, comps, post_smooth)
|
||
|
||
|
||
if __name__ == "__main__":
|
||
(results_df, delta_dict, model,
|
||
X_raw, Z_true, Z_hat, sigma, delay_map,
|
||
score, comps, post_smooth) = run_experiment()
|