"""F2-conf-02: OLS slope of y on x with HAC (Newey-West, Bartlett) standard errors.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py"""
import json, math
import numpy as np, pandas as pd
import statsmodels.api as sm
from scipy import stats

d = pd.read_csv("data/series.csv")
n_rows = len(d)
issues = []
# data checks
per = pd.PeriodIndex(d["month"], freq="M")
if d[["x", "y"]].isna().any().any():
    issues.append({"issue": "missing values", "handling": "rows dropped"})
    d = d.dropna(subset=["x", "y"])
if per.duplicated().any():
    issues.append({"issue": "duplicate months", "handling": "flagged"})
gaps = int(((per[1:] - per[:-1]).map(lambda o: o.n) != 1).sum())
if gaps:
    issues.append({"issue": f"{gaps} non-consecutive month steps", "handling": "flagged; HAC assumes equal spacing"})
d = d.sort_values("month").reset_index(drop=True)

X = sm.add_constant(d["x"].values)
y = d["y"].values
T = len(y)
ols = sm.OLS(y, X).fit()
alpha_hat, beta_hat = ols.params
se_iid = ols.bse[1]
u = ols.resid
rho_resid = float(np.sum(u[1:] * u[:-1]) / np.sum(u ** 2))

# Bandwidth: Andrews (1991) AR(1) plug-in for the Bartlett kernel, applied to the
# slope score v_t = (x_t - xbar) u_t. Data-dependent, adapts to the strong persistence.
v = (d["x"].values - d["x"].values.mean()) * u
rv = float(np.sum(v[1:] * v[:-1]) / np.sum(v[:-1] ** 2))
a1 = 4 * rv ** 2 / ((1 - rv) ** 2 * (1 + rv) ** 2)
andrews_bw = 1.1447 * (a1 * T) ** (1 / 3)
hac_lags = int(math.ceil(andrews_bw))  # Bartlett weights 1 - j/(L+1), j<=L
nw_rule = int(math.floor(4 * (T / 100) ** (2 / 9)))  # Newey-West (1994) rule of thumb

def hac(L):
    r = sm.OLS(y, X).fit(cov_type="HAC", cov_kwds={"maxlags": L, "use_correction": True})
    return float(r.bse[1])

se_hac = hac(hac_lags)
t_hac = beta_hat / se_hac
p_hac = 2 * stats.norm.sf(abs(t_hac))
z = stats.norm.ppf(0.975)
ci = (beta_hat - z * se_hac, beta_hat + z * se_hac)

sens = {}
for L in sorted({0, nw_rule, 8, 12, hac_lags, 18, 24, int(math.floor(0.75 * T ** (1 / 3)))}):
    s = hac(L)
    sens[L] = {"se": s, "t": beta_hat / s, "p_normal": 2 * stats.norm.sf(abs(beta_hat / s)),
               "p_t": 2 * stats.t.sf(abs(beta_hat / s), T - 2)}

res = {
    "task_id": "F2-conf-02",
    "beta_hat": float(beta_hat), "alpha_hat": float(alpha_hat),
    "se_iid": float(se_iid), "rho_resid": rho_resid,
    "se_hac": se_hac, "hac_lags": hac_lags,
    "t_hac": float(t_hac), "p_hac": float(p_hac),
    "beta_ci_low": float(ci[0]), "beta_ci_high": float(ci[1]),
    "memo_claim_supported": bool(p_hac < 0.05),
    "n_analysed": int(T), "feasibility": "complete", "feasibility_reason": None,
    "data_issues": issues, "n_input_rows": {"series.csv": int(n_rows)},
    "random_seed": None,
}
with open("out/results.json", "w") as f:
    json.dump(res, f, indent=2)
diag = {"t_iid": float(beta_hat / se_iid), "p_iid": float(ols.pvalues[1]),
        "rho_score": rv, "andrews_bw": andrews_bw, "nw_rule_lags": nw_rule,
        "sensitivity": {str(k): v for k, v in sens.items()}}
with open("out/diagnostics.json", "w") as f:
    json.dump(diag, f, indent=2)
print(json.dumps(res, indent=2)); print(json.dumps(diag, indent=2))