"""F2-conf-02: OLS slope of y on x with Newey-West HAC standard errors.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py"""
import json
import numpy as np
import 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
m = pd.PeriodIndex(d["month"], freq="M")
gaps = int(((m[1:] - m[:-1]).map(lambda o: o.n) != 1).sum())
if d[["x", "y"]].isna().any().any():
    issues.append({"issue": "missing values", "handling": "rows dropped"})
    d = d.dropna(subset=["x", "y"])
if d["month"].duplicated().any():
    issues.append({"issue": "duplicate months", "handling": "first kept"})
    d = d.drop_duplicates("month")
if gaps:
    issues.append({"issue": f"{gaps} gaps in monthly index", "handling": "kept; HAC lags count observations"})

X = sm.add_constant(d["x"].to_numpy())
y = d["y"].to_numpy()
n = 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
# score series v_t = (x_t - xbar) u_t, which is what the HAC long-run variance targets.
v = (d["x"].to_numpy() - d["x"].mean()) * u
rv = float(np.sum((v[1:] - v.mean()) * (v[:-1] - v.mean())) / np.sum((v - v.mean()) ** 2))
a1 = 4 * rv ** 2 / ((1 - rv) ** 2 * (1 + rv) ** 2)
hac_lags = int(np.floor(1.1447 * (a1 * n) ** (1 / 3)))
nw_rule = int(np.floor(4 * (n / 100) ** (2 / 9)))  # Newey-West (1994) rule of thumb, for sensitivity

def hac(L):
    r = sm.OLS(y, X).fit(cov_type="HAC", cov_kwds={"maxlags": L, "kernel": "bartlett", "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)
sens = {}
for L in sorted(set([nw_rule, hac_lags, 12, 18, 24])):
    s = hac(L)
    sens[str(L)] = {"se_hac": s, "t": beta_hat / s, "p": float(2 * stats.norm.sf(abs(beta_hat / s)))}

res = {
    "task_id": "F2-conf-02",
    "beta_hat": float(beta_hat),
    "alpha_hat": float(alpha_hat),
    "se_iid": float(se_iid),
    "t_iid": float(ols.tvalues[1]),
    "p_iid": float(ols.pvalues[1]),
    "rho_resid": rho_resid,
    "rho_score": rv,
    "se_hac": se_hac,
    "hac_lags": hac_lags,
    "hac_lags_nw_rule_of_thumb": nw_rule,
    "t_hac": float(t_hac),
    "p_hac": float(p_hac),
    "beta_ci_low": float(beta_hat - z * se_hac),
    "beta_ci_high": float(beta_hat + z * se_hac),
    "memo_claim_supported": bool(p_hac < 0.05),
    "hac_sensitivity": sens,
    "n_analysed": int(n),
    "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)
print(json.dumps(res, indent=2))