# Contract (P0)

Question. In a Gaussian AR(1), y_t = c + rho*y_{t-1} + e_t (c=0 in DGP), how biased is the OLS estimate of rho (regression on constant and y_{t-1}) in finite samples, and how well does the Marriott-Pope/Kendall approximation -(1+3rho)/n describe it at the design (n, rho)?

Estimands. (i) bias_analytical = -(1+3rho)/n evaluated at design values (deterministic). (ii) bias_mc = E[rho_hat] - rho estimated as the MC mean over R replications minus rho, with MC s.e. sd(rho_hat)/sqrt(R). Meaningful under: Gaussian iid innovations, |rho|<1, stationary start, OLS with intercept using t=2..n (n-1 effective obs). The analytical formula is a first-order (O(1/n)) asymptotic expansion of the bias; error is O(n^-2), so it need not match exactly at small n.

Outputs. out/results.json keys: task_id, bias_analytical, bias_mc, bias_mc_se, rho_hat_mean, rho_hat_sd_mc, discrepancy_se_units, se_asymptotic, n_replications, feasibility, feasibility_reason, data_issues, n_input_rows, n_analysed, random_seed. Plus out/report.md (6 sections), out/analysis.py, out/claims.json, state files, exclusions.csv.

Information rules. Only data/design.csv; follow design exactly (n=30, rho=0.8, sigma=1, intercept, stationary y_1, R=20000, seed 20261029 via numpy default_rng). Fresh series each replication.

Invalidity. Missing/inconsistent design params; non-stationary rho (|rho|>=1 makes stationary init impossible); not using the given seed; deviating from the regression spec.