"""F5-conf-02: finite-sample bias of OLS AR(1) coefficient. Regenerates out/results.json from data/ only."""
import json, os, hashlib
import numpy as np
import pandas as pd

ROOT = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
DATA = os.path.join(ROOT, "data", "design.csv")
OUT = os.path.join(ROOT, "out")

df = pd.read_csv(DATA)
d = dict(zip(df["parameter"].astype(str).str.strip(), df["value"].astype(str).str.strip()))
issues = []
required = ["n", "rho", "sigma", "intercept", "initial_condition", "n_replications", "seed"]
missing = [k for k in required if k not in d]
if missing:
    raise SystemExit(f"design missing parameters: {missing}")
if df["parameter"].duplicated().any():
    issues.append({"issue": "duplicated parameter rows", "handling": "first occurrence used"})

n = int(d["n"]); rho = float(d["rho"]); sigma = float(d["sigma"])
R = int(d["n_replications"]); seed = int(d["seed"])
assert d["intercept"].lower() == "yes" and d["initial_condition"].lower() == "stationary"
assert abs(rho) < 1 and sigma > 0 and n >= 3 and R >= 2

# ---- Simulation (c = 0). Draw order: y_1 for all reps, then innovations (R x (n-1)).
rng = np.random.default_rng(seed)
y = np.empty((R, n))
y[:, 0] = rng.normal(0.0, sigma / np.sqrt(1.0 - 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]

# ---- OLS of y_t on (1, y_{t-1}), t = 2..n  (slope = demeaned cross-product ratio)
x = y[:, :-1]; z = y[:, 1:]
xc = x - x.mean(axis=1, keepdims=True); zc = z - z.mean(axis=1, keepdims=True)
rho_hat = (xc * zc).sum(axis=1) / (xc * xc).sum(axis=1)

# cross-check one replication with lstsq
X0 = np.column_stack([np.ones(n - 1), x[0]])
b0 = np.linalg.lstsq(X0, z[0], rcond=None)[0]
assert abs(b0[1] - rho_hat[0]) < 1e-10

finite = np.isfinite(rho_hat)
n_excl = int((~finite).sum())
rho_hat_used = rho_hat[finite]
Rused = rho_hat_used.size

mean_ = float(rho_hat_used.mean())
sd_ = float(rho_hat_used.std(ddof=1))
bias_mc = mean_ - rho
bias_mc_se = sd_ / np.sqrt(Rused)
bias_an = -(1 + 3 * rho) / n
se_asy = float(np.sqrt((1 - rho**2) / n))

# supplementary (not required keys): formula with effective sample size n-1, median bias
bias_an_nm1 = -(1 + 3 * rho) / (n - 1)

results = {
    "task_id": "F5-conf-02",
    "bias_analytical": bias_an,
    "bias_mc": bias_mc,
    "bias_mc_se": float(bias_mc_se),
    "rho_hat_mean": mean_,
    "rho_hat_sd_mc": sd_,
    "discrepancy_se_units": float((bias_mc - bias_an) / bias_mc_se),
    "se_asymptotic": se_asy,
    "n_replications": int(R),
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": issues,
    "n_input_rows": {"design.csv": int(len(df))},
    "n_analysed": int(Rused),
    "random_seed": seed,
    # supplementary diagnostics
    "supp_bias_analytical_n_minus_1": bias_an_nm1,
    "supp_discrepancy_se_units_n_minus_1": float((bias_mc - bias_an_nm1) / bias_mc_se),
    "supp_bias_mc_ci95_lower": float(bias_mc - 1.96 * bias_mc_se),
    "supp_bias_mc_ci95_upper": float(bias_mc + 1.96 * bias_mc_se),
    "supp_relative_error_analytical": float((bias_an - bias_mc) / bias_mc),
    "supp_rho_hat_median": float(np.median(rho_hat_used)),
    "supp_frac_rho_hat_ge_1": float((rho_hat_used >= 1).mean()),
    "supp_sd_ratio_mc_to_asymptotic": float(sd_ / se_asy),
    "supp_n_nonfinite_excluded": n_excl,
    "supp_design_sha256": hashlib.sha256(open(DATA, "rb").read()).hexdigest(),
}

os.makedirs(OUT, exist_ok=True)
with open(os.path.join(OUT, "results.json"), "w") as f:
    json.dump(results, f, indent=2)
pd.DataFrame([
    {"step": "S0", "rule": "Monte Carlo replications simulated", "n_before": R, "n_after": R, "n_removed": 0,
     "rationale": "all R replications from design"},
    {"step": "S1", "rule": "drop replications with non-finite rho_hat", "n_before": R, "n_after": Rused,
     "n_removed": n_excl, "rationale": "degenerate regressor would make OLS undefined"},
]).to_csv(os.path.join(OUT, "exclusions.csv"), index=False)
print(json.dumps({k: results[k] for k in ["bias_analytical", "bias_mc", "bias_mc_se", "discrepancy_se_units"]}, indent=2))