"""F5-conf-02: Finite-sample bias of OLS AR(1) coefficient. Reads only data/design.csv."""
import json, hashlib, os
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")

raw = open(DATA, "rb").read()
sha = hashlib.sha256(raw).hexdigest()
d = pd.read_csv(DATA)
n_rows = int(len(d))
issues = []
if d["parameter"].duplicated().any():
    issues.append({"issue": "duplicated parameter names", "handling": "first occurrence used"})
p = dict(zip(d["parameter"].str.strip(), d["value"].astype(str).str.strip()))
required = ["n", "rho", "sigma", "intercept", "initial_condition", "n_replications", "seed"]
missing = [k for k in required if k not in p]
if missing:
    raise SystemExit(f"design missing parameters: {missing}")

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

# ---- analytical approximation and baseline ----
bias_analytical = -(1 + 3 * rho) / n
bias_analytical_n_minus_1 = -(1 + 3 * rho) / (n - 1)   # sensitivity: effective sample size
se_asymptotic = np.sqrt((1 - rho ** 2) / n)

# ---- Monte Carlo (vectorised, c = 0) ----
rng = np.random.default_rng(seed)
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]
x = y[:, :-1]; z = y[:, 1:]                       # regress y_t on (1, y_{t-1}), t=2..n
xc = x - x.mean(axis=1, keepdims=True)
zc = z - z.mean(axis=1, keepdims=True)
rho_hat = (xc * zc).sum(axis=1) / (xc ** 2).sum(axis=1)   # OLS slope with intercept

finite = np.isfinite(rho_hat)
n_excl = int((~finite).sum())
rho_hat = rho_hat[finite]
n_an = int(rho_hat.size)
mean_rh = float(rho_hat.mean())
sd_rh = float(rho_hat.std(ddof=1))
bias_mc = mean_rh - rho
bias_mc_se = float(sd_rh / np.sqrt(n_an))
disc = float((bias_mc - bias_analytical) / bias_mc_se)

# extra diagnostics (not required keys; written to separate file)
diag = {
    "design_sha256": sha,
    "bias_analytical_n_minus_1": bias_analytical_n_minus_1,
    "discrepancy_se_units_n_minus_1": float((bias_mc - bias_analytical_n_minus_1) / bias_mc_se),
    "bias_mc_ci95": [bias_mc - 1.96 * bias_mc_se, bias_mc + 1.96 * bias_mc_se],
    "rho_hat_median": float(np.median(rho_hat)),
    "share_rho_hat_below_rho": float((rho_hat < rho).mean()),
    "ratio_sd_mc_to_se_asymptotic": float(sd_rh / se_asymptotic),
    "relative_error_analytical_vs_mc": float((bias_analytical - bias_mc) / bias_mc),
    "n_nonfinite_excluded": n_excl,
}

results = {
    "task_id": "F5-conf-02",
    "bias_analytical": bias_analytical,
    "bias_mc": bias_mc,
    "bias_mc_se": bias_mc_se,
    "rho_hat_mean": mean_rh,
    "rho_hat_sd_mc": sd_rh,
    "discrepancy_se_units": disc,
    "se_asymptotic": float(se_asymptotic),
    "n_replications": R,
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": issues,
    "n_input_rows": {"design.csv": n_rows},
    "n_analysed": n_an,
    "random_seed": seed,
}
os.makedirs(OUT, exist_ok=True)
with open(os.path.join(OUT, "results.json"), "w") as f:
    json.dump(results, f, indent=2)
with open(os.path.join(OUT, "diagnostics.json"), "w") as f:
    json.dump(diag, f, indent=2)
pd.DataFrame([{"step": 1, "rule": "drop replications with non-finite rho_hat",
               "n_before": R, "n_after": n_an, "n_removed": n_excl,
               "rationale": "degenerate regressor (zero variance) would make OLS undefined"}]
             ).to_csv(os.path.join(OUT, "exclusions.csv"), index=False)
print(json.dumps(results, indent=2)); print(json.dumps(diag, indent=2))