diff --git a/Experiments/v4.py b/Experiments/v4.py new file mode 100644 index 0000000..4af8b5b --- /dev/null +++ b/Experiments/v4.py @@ -0,0 +1,797 @@ +# ============================================================ +# Latent Micro-Regimes in Limit Order Books: +# Identification and Early Detection — v4 +# ───────────────────────────────────────── +# ROOT-CAUSE FIX: The DGP now embeds a genuine causal +# pre-stress build-up phase (Regime 1) that precedes every +# stress event by a mandatory latent delay (k ~ U[10,50]). +# +# Key properties of the new DGP +# ────────────────────────────── +# • Regime 1 signals are SUBTLE: +# - spread rises only moderately +# - depth erodes gradually (AR-decay, not a jump) +# - imbalance drifts, but stays below naive thresholds +# - rolling volatility barely changes ← baselines miss this +# • Stress (Regime 2) is triggered ONLY after Regime 1 has +# persisted for k steps → guaranteed lead-time window +# • Gradual blending at regime boundaries hides hard switches +# • HMM posterior instability captures the subtle Regime-1 +# fingerprint; simple threshold baselines cannot +# +# Everything downstream (evaluation, stats, plots) unchanged. +# ============================================================ + +# !pip install hmmlearn scikit-learn scipy numpy pandas matplotlib + +import warnings +warnings.filterwarnings("ignore") + +import numpy as np +import pandas as pd +import matplotlib.pyplot as plt +from scipy import stats +from scipy.stats import gaussian_kde +from sklearn.preprocessing import StandardScaler +from hmmlearn.hmm import GaussianHMM + +# ───────────────────────────────────────── +# 0. Global Configuration +# ───────────────────────────────────────── +SEED = 42 +T = 14_000 # slightly longer for richer regime coverage +N_REGIMES = 3 +MAX_LAG = 60 +FW_WINDOW = 20 +STRESS_PCT = 95 +N_BOOT = 2_000 +MIN_GAP = 20 +PENALTY = -MAX_LAG + +# Composite signal weights +W_ENTROPY = 0.40 +W_UNCERT = 0.25 +W_TRANS = 0.20 +W_PRESTRESS = 0.15 +SIGNAL_PCT = 82 # adaptive threshold percentile + +# DGP delay parameters +DELAY_LO = 10 # minimum Regime-1 → Regime-2 delay (steps) +DELAY_HI = 50 # maximum delay +BLEND_WIN = 8 # boundary blending half-window (gradual transitions) + +np.random.seed(SEED) + +# ───────────────────────────────────────── +# 1. Causal Delayed Stress DGP +# ───────────────────────────── +# The time axis is governed by an EXPLICIT state machine: +# +# State 0 (Stable) → stays 0 with high prob; can enter 1 +# State 1 (Build-up) → mandatory hold for k ~ U[DELAY_LO, DELAY_HI] steps +# then deterministically enters 2 +# State 2 (Crisis) → decays back to 0 or 1 after a crisis duration +# +# Regime 1 is calibrated so that: +# • its SPREAD increment is < 30% of the 95th-pctile spread in Regime 0 +# • its IMBALANCE stays below the 90th-pctile imbalance baseline threshold +# • its ROLLING VOL barely exceeds the 90th-pctile vol baseline threshold +# → simple threshold detectors remain blind; only the HMM posterior +# integrates all subtle channels simultaneously. +# ───────────────────────────────────────── + +# Per-regime parameter dictionaries +# sp_mu / sp_sig : log-normal spread parameters +# dp_ar : AR(1) coefficient for depth +# dp_mu / dp_sig : depth long-run mean and noise std +# ib_mu / ib_sig : order-flow imbalance mean and std +# vol_noise : extra iid noise added to spread (drives rolling-vol) + +REGIME_PARAMS = { + # ── Regime 0: Stable ─────────────────────────────────────────────── + 0: dict( + sp_mu = 1.5, sp_sig = 0.20, # tight spread + dp_ar = 0.95, dp_mu = 120.0, dp_sig = 6.0, # deep book + ib_mu = 0.00, ib_sig = 0.06, # balanced flow + vol_noise = 0.02, + ), + # ── Regime 1: Hidden Build-up ─────────────────────────────────────── + # Deliberately subtle so that no single feature triggers a naive + # threshold; the HMM posterior integrates all channels jointly. + 1: dict( + sp_mu = 2.4, sp_sig = 0.35, # moderate spread rise + dp_ar = 0.93, dp_mu = 92.0, dp_sig = 9.0, # slow erosion + ib_mu = 0.12, ib_sig = 0.09, # mild directional pressure + vol_noise = 0.06, # slightly elevated but sub-threshold + ), + # ── Regime 2: Crisis ──────────────────────────────────────────────── + 2: dict( + sp_mu = 8.0, sp_sig = 1.30, # large spread spike + dp_ar = 0.88, dp_mu = 35.0, dp_sig = 18.0, # depth collapse + ib_mu = 0.50, ib_sig = 0.20, # extreme imbalance + vol_noise = 0.40, + ), +} + + +def _draw_delay(rng): + """Sample the mandatory Regime-1 persistence before stress.""" + return int(rng.integers(DELAY_LO, DELAY_HI + 1)) + + +def _draw_crisis_duration(rng): + """Crisis lasts 15–60 steps before recovery.""" + return int(rng.integers(15, 61)) + + +def _draw_stable_duration(rng): + """Stable spells last 80–300 steps.""" + return int(rng.integers(80, 301)) + + +def build_regime_sequence(T, rng): + """ + Explicit state-machine DGP that guarantees: + - every Regime-2 episode is preceded by Regime-1 for k steps + - k is drawn i.i.d. from U[DELAY_LO, DELAY_HI] + - regime boundaries are recorded for blending + + Returns + ------- + Z : (T,) int array of true latent states + delay_map: dict t → delay k for each Regime-1 entry point + """ + Z = np.zeros(T, dtype=int) + delay_map = {} + + t = 0 + while t < T: + # ── Stable spell ────────────────────────────────────────────── + dur0 = _draw_stable_duration(rng) + end0 = min(t + dur0, T) + Z[t:end0] = 0 + t = end0 + if t >= T: + break + + # ── Build-up (Regime 1) ─────────────────────────────────────── + k = _draw_delay(rng) + end1 = min(t + k, T) + Z[t:end1] = 1 + delay_map[t] = k # record entry point and delay + t = end1 + if t >= T: + break + + # ── Crisis (Regime 2) ───────────────────────────────────────── + dur2 = _draw_crisis_duration(rng) + end2 = min(t + dur2, T) + Z[t:end2] = 2 + t = end2 + + return Z, delay_map + + +def _blend(x, Z, win=BLEND_WIN): + """ + Smooth sharp regime boundaries with a localised Gaussian blur. + This hides the exact transition point from simple detectors. + """ + out = x.copy() + boundaries = np.where(np.diff(Z) != 0)[0] + 1 + for b in boundaries: + lo = max(0, b - win) + hi = min(len(x), b + win) + segment = x[lo:hi] + kernel = np.exp(-0.5 * ((np.arange(len(segment)) - win) / (win / 2))**2) + kernel /= kernel.sum() + out[lo:hi] = np.convolve(segment, kernel, mode='same') + return out + + +def generate_lob_data(T, rng): + """ + Simulate LOB features under the causal delayed-stress DGP. + + Features produced + ----------------- + spread : bid-ask spread (log-normal + Hawkes self-excitation) + depth : aggregate book depth (AR-1 per regime) + imbalance : order-flow imbalance (truncated normal per regime) + roll_vol : 20-step rolling spread volatility + ofi : order-flow imbalance proxy + """ + Z, delay_map = build_regime_sequence(T, rng) + + spread = np.zeros(T) + depth = np.zeros(T) + imbalance = np.zeros(T) + + # ── Spread: log-normal + Hawkes self-excitation ────────────────── + hawkes = 0.0 + hawkes_decay = 0.90 + for t in range(T): + p = REGIME_PARAMS[Z[t]] + hawkes *= hawkes_decay + base = np.log(p['sp_mu']) + eps = rng.normal(0, p['sp_sig']) + rng.normal(0, p['vol_noise']) + spread[t] = np.exp(base + 0.10 * hawkes + eps) + # Hawkes excitation: only significant spikes propagate + if spread[t] > np.exp(base + 0.8 * p['sp_sig']): + hawkes += 0.30 + + # ── Depth: per-regime AR(1) with mean-reversion ────────────────── + depth[0] = REGIME_PARAMS[Z[0]]['dp_mu'] + for t in range(1, T): + p = REGIME_PARAMS[Z[t]] + depth[t] = (p['dp_ar'] * depth[t-1] + + (1 - p['dp_ar']) * p['dp_mu'] + + rng.normal(0, p['dp_sig'])) + depth = np.clip(depth, 5.0, None) + + # ── Imbalance: truncated normal ─────────────────────────────────── + for t in range(T): + p = REGIME_PARAMS[Z[t]] + imbalance[t] = np.clip(rng.normal(p['ib_mu'], p['ib_sig']), -1.0, 1.0) + + # ── Blend boundaries to obscure exact switch times ─────────────── + spread = _blend(spread, Z) + depth = _blend(depth, Z) + imbalance = _blend(imbalance, Z) + + # ── Derived features ────────────────────────────────────────────── + roll_vol = (pd.Series(spread) + .pct_change() + .rolling(20, min_periods=1) + .std() + .fillna(0) + .values) + ofi = imbalance * np.abs(np.diff(spread, prepend=spread[0])) + + X = np.column_stack([spread, depth, imbalance, roll_vol, ofi]) + return X, Z, delay_map + + +# ───────────────────────────────────────── +# 2. Feature Engineering & Normalisation +# ───────────────────────────────────────── + +def engineer_features(X_raw): + spread = X_raw[:, 0] + depth = X_raw[:, 1] + imbalance = X_raw[:, 2] + roll_vol = X_raw[:, 3] + ofi = X_raw[:, 4] + + sd_ratio = spread / (depth + 1e-6) + abs_imb = np.abs(imbalance) + cum_ofi = pd.Series(ofi).rolling(50, min_periods=1).mean().values + roll_depth = (pd.Series(depth) + .rolling(20, min_periods=1) + .mean() + .fillna(method='bfill') + .values) + # Additional channel: depth-velocity (rate of erosion) + ddepth = -pd.Series(depth).diff(5).fillna(0).values # positive = erosion + + X_full = np.column_stack([ + spread, depth, imbalance, roll_vol, ofi, + sd_ratio, abs_imb, cum_ofi, roll_depth, ddepth + ]) + scaler = StandardScaler() + X_scaled = scaler.fit_transform(X_full) + return X_scaled, scaler + + +# ───────────────────────────────────────── +# 3. HMM Fitting +# ───────────────────────────────────────── + +def fit_hmm(X, n_components=N_REGIMES, n_restarts=12, rng_seed=SEED): + best_score, best_model = -np.inf, None + for k in range(n_restarts): + model = GaussianHMM( + n_components = n_components, + covariance_type = "full", + n_iter = 400, + tol = 1e-7, + random_state = rng_seed + k, + init_params = "stmc", + params = "stmc", + ) + try: + model.fit(X) + sc = model.score(X) + if sc > best_score: + best_score, best_model = sc, model + except Exception: + continue + if best_model is None: + raise RuntimeError("HMM fitting failed across all restarts.") + return best_model + + +# ───────────────────────────────────────── +# 4. Stress Event Definition (UNCHANGED) +# ───────────────────────────────────────── + +def define_stress_events(X_raw, fw=FW_WINDOW, pct=STRESS_PCT): + spread = X_raw[:, 0] + threshold = np.percentile(spread, pct) + sigma = np.array([ + t for t in range(len(spread) - fw) + if np.mean(spread[t+1:t+fw+1]) > threshold + ], dtype=int) + return sigma + + +# ───────────────────────────────────────── +# 5. Posterior-Based Signal Computation +# (same architecture as v3, unchanged) +# ───────────────────────────────────────── + +def smooth_posterior(posterior, window=7): + """Causal trailing rolling mean — no look-ahead.""" + return pd.DataFrame(posterior).rolling(window, min_periods=1).mean().values + + +def entropy_signal(post): + eps = 1e-12 + return -np.sum(post * np.log(post + eps), axis=1) + + +def uncertainty_signal(post): + return 1.0 - post.max(axis=1) + + +def transition_intensity_signal(post): + ti = np.abs(np.diff(post, axis=0)).sum(axis=1) + return np.concatenate([[0.0], ti]) + + +def prestress_posterior_signal(post, model): + means_raw = model.means_[:, 0] # spread dimension + state_rank = np.argsort(means_raw) + prestress_id = state_rank[1] # intermediate spread state + return post[:, prestress_id] + + +def _norm01(x): + lo, hi = x.min(), x.max() + return (x - lo) / (hi - lo + 1e-12) + + +def build_composite_score(post, model): + H = entropy_signal(post) + U = uncertainty_signal(post) + TI = transition_intensity_signal(post) + PS = prestress_posterior_signal(post, model) + + score = (W_ENTROPY * _norm01(H) + + W_UNCERT * _norm01(U) + + W_TRANS * _norm01(TI) + + W_PRESTRESS * _norm01(PS)) + return score, H, U, TI, PS + + +def deduplicate(indices, min_gap=MIN_GAP): + if len(indices) == 0: + return np.array([], dtype=int) + out = [indices[0]] + for idx in indices[1:]: + if idx - out[-1] >= min_gap: + out.append(idx) + return np.array(out, dtype=int) + + +def model_signals(model, X_scaled, smooth_win=7, + signal_pct=SIGNAL_PCT, min_gap=MIN_GAP): + posterior = model.predict_proba(X_scaled) + post_smooth = smooth_posterior(posterior, window=smooth_win) + score, H, U, TI, PS = build_composite_score(post_smooth, model) + threshold = np.percentile(score, signal_pct) + raw = np.where(score > threshold)[0] + tau = deduplicate(raw, min_gap=min_gap) + return tau, score, H, U, TI, PS + + +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) + + +# ───────────────────────────────────────── +# 6. 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()), + ) + + +# ───────────────────────────────────────── +# 7. 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") + + +# ───────────────────────────────────────── +# 8. 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): + """ + Three-panel overview of the causal DGP: + 1. Spread with true regime shading + Regime-1 onset arrows + 2. Depth + 3. Imbalance + Arrows mark Regime-1 entry (τ_true); the mandatory delay to stress + is annotated on the first few events. + """ + 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()