542 lines
21 KiB
Python
542 lines
21 KiB
Python
# ============================================================
|
||
# Latent Micro-Regimes in Limit Order Books:
|
||
# Identification and Early Detection — v2
|
||
# ─────────────────────────────────────────
|
||
# Key changes over v1:
|
||
# 1. Regime 1 = pre-stress build-up, Regime 2 = crisis
|
||
# → HMM entry into regime 1 is the early-warning signal
|
||
# 2. Detection via posterior ENTROPY rise, not hard-switch
|
||
# 3. Minimum-gap deduplication (no signal flooding)
|
||
# 4. Posterior probability smoothing for cleaner signals
|
||
# 5. Baselines use identical deduplication
|
||
# ============================================================
|
||
# !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 = 12_000
|
||
N_REGIMES = 3
|
||
MAX_LAG = 60 # evaluation window (timesteps)
|
||
FW_WINDOW = 20 # forward window for stress label
|
||
STRESS_PCT = 95 # percentile for stress threshold
|
||
N_BOOT = 2_000
|
||
MIN_GAP = 15 # minimum timesteps between two signals (dedup)
|
||
PENALTY = -MAX_LAG
|
||
|
||
np.random.seed(SEED)
|
||
|
||
# ─────────────────────────────────────────
|
||
# 1. Structured Latent Regime Generator
|
||
# Regime 0 = Normal (baseline, calm)
|
||
# Regime 1 = Pre-stress build-up ← the key early-warning state
|
||
# Regime 2 = Crisis / stress peak
|
||
#
|
||
# Causal chain: 0 → 1 → 2 → (0 or 1)
|
||
# The HMM must learn that regime 1 is a harbinger of regime 2.
|
||
# We encode this by:
|
||
# • Making spread/depth in regime 1 intermediate
|
||
# • Making transitions 0→1 more likely than 0→2 directly
|
||
# • Stress events defined on FUTURE spread (no leakage)
|
||
# ─────────────────────────────────────────
|
||
|
||
REGIME_PARAMS = {
|
||
# spread: mu, sigma (log-normal)
|
||
# depth: mu, sigma (AR-1)
|
||
# imb: mu, sigma (truncated normal)
|
||
# vol_base: scaling factor
|
||
0: dict(sp_mu=1.5, sp_sig=0.25, dp_mu=120, dp_sig=10, ib_mu=0.00, ib_sig=0.07, vb=0.35),
|
||
1: dict(sp_mu=3.2, sp_sig=0.55, dp_mu= 88, dp_sig=16, ib_mu=0.22, ib_sig=0.13, vb=1.10),
|
||
2: dict(sp_mu=7.5, sp_sig=1.20, dp_mu= 42, dp_sig=22, ib_mu=0.48, ib_sig=0.22, vb=2.90),
|
||
}
|
||
|
||
def build_causal_transition_matrix() -> np.ndarray:
|
||
"""
|
||
Transition matrix with causal structure:
|
||
- 0 → 1 much more likely than 0 → 2 (stress builds gradually)
|
||
- 1 → 2 is the crisis trigger
|
||
- 2 → 0 or 1 (recovery)
|
||
"""
|
||
P = np.array([
|
||
[0.970, 0.028, 0.002], # Normal → mostly stays
|
||
[0.060, 0.900, 0.040], # Pre-stress → can escalate
|
||
[0.100, 0.150, 0.750], # Crisis → decays back
|
||
])
|
||
# Normalise rows (safety)
|
||
return P / P.sum(axis=1, keepdims=True)
|
||
|
||
|
||
def simulate_latent_chain(T, P, pi0, rng):
|
||
K = P.shape[0]
|
||
Z = np.empty(T, dtype=int)
|
||
Z[0] = rng.choice(K, p=pi0)
|
||
for t in range(1, T):
|
||
Z[t] = rng.choice(K, p=P[Z[t - 1]])
|
||
return Z
|
||
|
||
|
||
def generate_lob_data(T, rng):
|
||
"""
|
||
Simulate LOB features under a causal Markov-switching model.
|
||
|
||
Hawkes-like self-excitation on spread ensures bursts cluster
|
||
without trivially revealing regime via a single feature.
|
||
"""
|
||
P = build_causal_transition_matrix()
|
||
pi0 = np.array([0.85, 0.12, 0.03])
|
||
Z = simulate_latent_chain(T, P, pi0, rng)
|
||
|
||
spread = np.zeros(T)
|
||
depth = np.zeros(T)
|
||
imbalance = np.zeros(T)
|
||
|
||
# Spread: log-normal + Hawkes excitation
|
||
hawkes = 0.0
|
||
decay = 0.88
|
||
for t in range(T):
|
||
p = REGIME_PARAMS[Z[t]]
|
||
hawkes = hawkes * decay
|
||
eps = rng.normal(0, p['sp_sig'])
|
||
spread[t] = np.exp(np.log(p['sp_mu']) + 0.12 * hawkes + eps)
|
||
if spread[t] > np.exp(np.log(p['sp_mu']) + p['sp_sig']):
|
||
hawkes += 0.25
|
||
|
||
# Depth: mean-reverting AR(1)
|
||
phi = 0.93
|
||
depth[0] = REGIME_PARAMS[Z[0]]['dp_mu']
|
||
for t in range(1, T):
|
||
p = REGIME_PARAMS[Z[t]]
|
||
depth[t] = phi * depth[t-1] + (1-phi) * p['dp_mu'] + rng.normal(0, p['dp_sig'])
|
||
depth = np.clip(depth, 5, 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, 1)
|
||
|
||
# Rolling spread vol (20-step)
|
||
roll_vol = pd.Series(spread).pct_change().rolling(20).std().fillna(0).values
|
||
|
||
# OFI proxy
|
||
ofi = imbalance * np.abs(np.diff(spread, prepend=spread[0]))
|
||
|
||
X = np.column_stack([spread, depth, imbalance, roll_vol, ofi])
|
||
return X, Z
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 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).mean().fillna(method='bfill').values
|
||
|
||
X_full = np.column_stack([
|
||
spread, depth, imbalance, roll_vol, ofi,
|
||
sd_ratio, abs_imb, cum_ofi, roll_depth
|
||
])
|
||
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=10, 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 = 300,
|
||
tol = 1e-6,
|
||
random_state = rng_seed + k,
|
||
init_params = "stmc",
|
||
params = "stmc",
|
||
)
|
||
try:
|
||
model.fit(X)
|
||
score = model.score(X)
|
||
if score > best_score:
|
||
best_score, best_model = score, model
|
||
except Exception:
|
||
continue
|
||
if best_model is None:
|
||
raise RuntimeError("HMM fitting failed.")
|
||
return best_model
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 4. Stress Event Definition (no leakage)
|
||
# ─────────────────────────────────────────
|
||
|
||
def define_stress_events(X_raw, fw=FW_WINDOW, pct=STRESS_PCT):
|
||
spread = X_raw[:, 0]
|
||
threshold = np.percentile(spread, pct)
|
||
sigma = [t for t in range(len(spread) - fw)
|
||
if np.mean(spread[t+1:t+fw+1]) > threshold]
|
||
return np.array(sigma, dtype=int)
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 5. Signal Computation (the core upgrade)
|
||
# ─────────────────────────────────────────
|
||
|
||
def state_entropy(posterior):
|
||
"""Shannon entropy of the posterior state distribution at each step."""
|
||
eps = 1e-12
|
||
return -np.sum(posterior * np.log(posterior + eps), axis=1)
|
||
|
||
|
||
def deduplicate(indices, min_gap=MIN_GAP):
|
||
"""
|
||
Keep only the FIRST index in each cluster of indices
|
||
that are within min_gap of each other.
|
||
This prevents signal flooding.
|
||
"""
|
||
if len(indices) == 0:
|
||
return indices
|
||
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, Z_hat,
|
||
entropy_pct=80, smooth_window=5, min_gap=MIN_GAP):
|
||
"""
|
||
Uncertainty-based early-warning signal.
|
||
|
||
Strategy (three complementary triggers, unioned then deduped):
|
||
A) Entropy spike: posterior uncertainty rises sharply
|
||
→ captures "the HMM is unsure", a known pre-transition marker
|
||
B) Pre-stress state entry: Z_hat transitions INTO the intermediate
|
||
state (state with 2nd-highest mean spread)
|
||
→ aligns detection with causal regime structure
|
||
C) Entropy trend: rolling entropy slope turns positive
|
||
→ catches gradual build-up before a hard switch
|
||
|
||
All triggers are deduplicated so N(τ) stays controlled.
|
||
"""
|
||
posterior = model.predict_proba(X_scaled) # (T, K)
|
||
|
||
# ── Smooth posterior to reduce HMM jitter ──
|
||
smooth_post = pd.DataFrame(posterior).rolling(
|
||
smooth_window, min_periods=1, center=True).mean().values
|
||
|
||
entropy = state_entropy(smooth_post)
|
||
|
||
# ── Identify the "pre-stress" HMM state ──
|
||
# We rank states by their mean spread (feature 0 in raw space)
|
||
means_raw = model.means_[:, 0] # spread dim of HMM means
|
||
state_rank = np.argsort(means_raw) # [low, mid, high]
|
||
prestress_state = state_rank[1] # intermediate spread state
|
||
|
||
# ── Trigger A: entropy spike ──
|
||
ent_thresh = np.percentile(entropy, entropy_pct)
|
||
sig_A = np.where(entropy > ent_thresh)[0]
|
||
|
||
# ── Trigger B: entry into pre-stress state ──
|
||
enters_prestress = (Z_hat[1:] == prestress_state) & (Z_hat[:-1] != prestress_state)
|
||
sig_B = np.where(enters_prestress)[0]
|
||
|
||
# ── Trigger C: entropy slope turns positive ──
|
||
ent_slope = pd.Series(entropy).diff(5).fillna(0).values
|
||
slope_thresh = np.percentile(ent_slope[ent_slope > 0], 70)
|
||
sig_C = np.where(ent_slope > slope_thresh)[0]
|
||
|
||
# ── Union + deduplicate ──
|
||
all_signals = np.unique(np.concatenate([sig_A, sig_B, sig_C]))
|
||
tau = deduplicate(all_signals, min_gap=min_gap)
|
||
return tau
|
||
|
||
|
||
def imbalance_baseline(X_raw, pct=90, min_gap=MIN_GAP):
|
||
imb = np.abs(X_raw[:, 2])
|
||
threshold = np.percentile(imb, pct)
|
||
raw = np.where(imb > threshold)[0]
|
||
return deduplicate(raw, min_gap=min_gap)
|
||
|
||
|
||
def volatility_baseline(X_raw, pct=90, min_gap=MIN_GAP):
|
||
roll_vol = X_raw[:, 3]
|
||
threshold = np.percentile(roll_vol, pct)
|
||
raw = np.where(roll_vol > threshold)[0]
|
||
return deduplicate(raw, min_gap=min_gap)
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 6. Lead-Time Evaluation
|
||
# ─────────────────────────────────────────
|
||
|
||
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
|
||
# ─────────────────────────────────────────
|
||
|
||
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. Publication-Quality 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,
|
||
})
|
||
|
||
|
||
def plot_entropy_and_regimes(X_raw, Z_true, Z_hat, entropy, tau_model,
|
||
sigma, n_show=2500):
|
||
"""
|
||
Four-panel diagnostic:
|
||
1. Spread with true regime shading
|
||
2. Posterior entropy (with signal thresholds and triggers marked)
|
||
3. Inferred HMM state
|
||
4. Depth with stress 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]
|
||
|
||
tau_vis = tau_model[tau_model < t_end]
|
||
sigma_vis = sigma[sigma < t_end]
|
||
|
||
regime_colors = {0: "#DDEEFF", 1: "#FFF3CD", 2: "#FFDDDD"}
|
||
|
||
fig, axes = plt.subplots(4, 1, figsize=(12, 9), sharex=True,
|
||
gridspec_kw={"height_ratios": [2, 2, 1, 2]})
|
||
|
||
# Panel 1 — Spread + true shading
|
||
ax = axes[0]
|
||
for k, c in regime_colors.items():
|
||
ax.fill_between(t_ax, 0, spread.max()*1.1,
|
||
where=Z_true[:t_end]==k, color=c, alpha=0.55,
|
||
label=f"State {k}")
|
||
ax.plot(t_ax, spread, lw=0.7, color="#1A1A2E")
|
||
ax.set_ylabel("Bid-Ask Spread")
|
||
ax.legend(loc="upper right", fontsize=8, frameon=False, ncol=3)
|
||
ax.set_title("True Regimes · Posterior Entropy · Inferred States · Market Depth",
|
||
fontsize=12, pad=8)
|
||
|
||
# Panel 2 — Entropy + model triggers
|
||
ax = axes[1]
|
||
ent_vis = entropy[:t_end]
|
||
ax.plot(t_ax, ent_vis, lw=0.9, color="#555555", alpha=0.85, label="Entropy")
|
||
ent_thresh = np.percentile(entropy, 80)
|
||
ax.axhline(ent_thresh, color="#FF8800", lw=1.0, ls="--", label="80th pct threshold")
|
||
ax.vlines(tau_vis, ent_vis.min(), ent_vis.max(),
|
||
color=PALETTE["Model"], lw=0.7, alpha=0.6, label="Model signal τ")
|
||
ax.set_ylabel("Posterior Entropy")
|
||
ax.legend(loc="upper right", fontsize=8, frameon=False)
|
||
|
||
# Panel 3 — Inferred HMM state
|
||
ax = axes[2]
|
||
ax.step(t_ax, Z_hat[:t_end], lw=0.9, color=PALETTE["Model"])
|
||
ax.set_ylabel("HMM State")
|
||
ax.set_yticks([0, 1, 2])
|
||
|
||
# Panel 4 — Depth + stress events
|
||
ax = axes[3]
|
||
ax.plot(t_ax, depth, lw=0.7, color="#2D6A4F")
|
||
ax.vlines(sigma_vis, depth.min(), depth.max(),
|
||
color=PALETTE["Imbalance"], lw=0.7, alpha=0.5, label="Stress event σ")
|
||
ax.set_ylabel("Market Depth")
|
||
ax.set_xlabel("Timestep")
|
||
ax.legend(loc="upper right", fontsize=8, frameon=False)
|
||
|
||
fig.tight_layout()
|
||
plt.show()
|
||
|
||
|
||
def plot_lead_time_densities(delta_dict, max_lag=MAX_LAG):
|
||
fig, ax = plt.subplots(figsize=(8, 4.5))
|
||
x_grid = np.linspace(-max_lag-5, max_lag+5, 600)
|
||
|
||
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=2.2, color=color, label=name)
|
||
ax.fill_between(x_grid, kde(x_grid), alpha=0.13, color=color)
|
||
pf = np.mean(deltas <= PENALTY)
|
||
ax.annotate(f"missed={pf:.1%}", xy=(-max_lag+1, 0.004*(i+1)),
|
||
color=color, fontsize=8.5)
|
||
|
||
ax.axvline(0, color="gray", lw=1.0, ls="--", label="Zero lead-time")
|
||
ax.set_xlabel("Lead time Δ (timesteps)", labelpad=8)
|
||
ax.set_ylabel("Density", labelpad=8)
|
||
ax.set_title("Lead-Time Distribution: Model vs Baselines", fontsize=13, pad=10)
|
||
ax.legend(frameon=False, fontsize=10)
|
||
ax.set_xlim(-max_lag-2, max_lag+2)
|
||
fig.tight_layout()
|
||
plt.show()
|
||
|
||
|
||
def plot_results_table(results_df):
|
||
fig, ax = plt.subplots(figsize=(11, 2.2))
|
||
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, 1.6)
|
||
for j in range(len(results_df.columns)):
|
||
tbl[0, j].set_facecolor("#2C6FAC")
|
||
tbl[0, j].set_text_props(color="white", fontweight="bold")
|
||
fig.tight_layout()
|
||
plt.show()
|
||
|
||
|
||
# ─────────────────────────────────────────
|
||
# 9. Main Pipeline
|
||
# ─────────────────────────────────────────
|
||
|
||
def run_experiment():
|
||
rng = np.random.default_rng(SEED)
|
||
|
||
print("=" * 62)
|
||
print(" Step 1 / 6 — Generating causal LOB data …")
|
||
X_raw, Z_true = generate_lob_data(T, rng)
|
||
dist = " | ".join([f"State {k}: {(Z_true==k).mean():.1%}" for k in range(N_REGIMES)])
|
||
print(f" {T:,} timesteps | {dist}")
|
||
|
||
print("\n Step 2 / 6 — Feature engineering …")
|
||
X_scaled, scaler = engineer_features(X_raw)
|
||
print(f" Feature matrix: {X_scaled.shape}")
|
||
|
||
print("\n Step 3 / 6 — Fitting HMM (10 restarts) …")
|
||
model = fit_hmm(X_scaled)
|
||
Z_hat = model.predict(X_scaled)
|
||
ll = model.score(X_scaled)
|
||
print(f" Best log-likelihood: {ll:,.2f} | Converged: {model.monitor_.converged}")
|
||
|
||
# Identify which HMM state corresponds to each true regime
|
||
# (sorted by mean spread value in the HMM)
|
||
means_sp = model.means_[:, 0]
|
||
state_rank = np.argsort(means_sp)
|
||
print(f" HMM state ranking by spread: {state_rank.tolist()} "
|
||
f"(low→high spread)")
|
||
|
||
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)")
|
||
|
||
print("\n Step 5 / 6 — Computing signals …")
|
||
# Model signals: uncertainty + pre-stress entry
|
||
posterior = model.predict_proba(X_scaled)
|
||
smooth_post = pd.DataFrame(posterior).rolling(5, min_periods=1, center=True).mean().values
|
||
entropy = state_entropy(smooth_post)
|
||
|
||
tau_model = model_signals(model, X_scaled, Z_hat)
|
||
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}
|
||
|
||
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}")
|
||
|
||
print("\n Rendering figures …")
|
||
plot_entropy_and_regimes(X_raw, Z_true, Z_hat, entropy, 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, entropy
|
||
|
||
|
||
if __name__ == "__main__":
|
||
(results_df, delta_dict, model,
|
||
X_raw, Z_true, Z_hat, sigma, entropy) = run_experiment()
|