"""F5-conf-02: Monte Carlo bias of OLS AR(1) coefficient vs Kendall/Marriott-Pope approximation.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py
"""
import json, os
import numpy as np
import pandas as pd

d = pd.read_csv("data/design.csv")
p = dict(zip(d["parameter"], d["value"]))
n = int(p["n"]); rho = float(p["rho"]); sigma = float(p["sigma"])
R = int(p["n_replications"]); seed = int(p["seed"])
issues = []
assert str(p["intercept"]).strip().lower() == "yes"
assert str(p["initial_condition"]).strip().lower() == "stationary"
if not (abs(rho) < 1 and n > 2 and R > 1 and sigma > 0):
    issues.append({"issue": "invalid design value", "handling": "none"})

rng = np.random.default_rng(seed)
# Draw order: y_1 for all replications, then innovations eps_2..eps_n (R x (n-1)).
y = np.empty((R, n))
y[:, 0] = rng.normal(0.0, sigma / np.sqrt(1 - rho**2), size=R)
eps = rng.normal(0.0, sigma, size=(R, n - 1))
for t in range(1, n):
    y[:, t] = rho * y[:, t - 1] + eps[:, t - 1]   # c = 0

x = y[:, :-1]; z = y[:, 1:]          # regressor y_{t-1}, response y_t, t=2..n
xd = x - x.mean(axis=1, keepdims=True)
zd = z - z.mean(axis=1, keepdims=True)
rho_hat = (xd * zd).sum(1) / (xd**2).sum(1)   # OLS slope with intercept

# sanity check vs. explicit lstsq on first replication
X0 = np.column_stack([np.ones(n - 1), x[0]])
assert np.isclose(np.linalg.lstsq(X0, z[0], rcond=None)[0][1], rho_hat[0])

ok = np.isfinite(rho_hat)
rh = rho_hat[ok]
mean = float(rh.mean()); sd = float(rh.std(ddof=1)); se = sd / np.sqrt(rh.size)
bias_an = -(1 + 3 * rho) / n
bias_mc = mean - rho
# For reference: same formula using the effective regression sample size n-1
bias_an_nm1 = -(1 + 3 * rho) / (n - 1)

res = {
    "task_id": "F5-conf-02",
    "bias_analytical": bias_an,
    "bias_mc": bias_mc,
    "bias_mc_se": se,
    "rho_hat_mean": mean,
    "rho_hat_sd_mc": sd,
    "discrepancy_se_units": (bias_mc - bias_an) / se,
    "se_asymptotic": float(np.sqrt((1 - rho**2) / n)),
    "n_replications": R,
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": issues,
    "n_input_rows": {"design.csv": int(len(d))},
    "n_analysed": int(rh.size),
    "random_seed": seed,
    # supplementary (not required)
    "bias_analytical_n_minus_1": bias_an_nm1,
    "discrepancy_se_units_n_minus_1": (bias_mc - bias_an_nm1) / se,
    "rho_hat_median": float(np.median(rh)),
    "share_rho_hat_below_rho": float((rh < rho).mean()),
    "relative_discrepancy": (bias_mc - bias_an) / abs(bias_an),
}
os.makedirs("out", exist_ok=True)
with open("out/results.json", "w") as f:
    json.dump(res, f, indent=2)
print(json.dumps(res, indent=2))