# Contract (P0) — F5-conf-02

Question. Finite-sample bias of OLS rho_hat (y_t on 1, y_{t-1}, t=2..n) in Gaussian AR(1), c=0, compared with the Marriott–Pope/Kendall approximation -(1+3rho)/n. Estimands. (i) bias_analytical = -(1+3rho)/n at design (n=30, rho=0.8) — a first-order (O(1/n)) asymptotic expansion of E[rho_hat]-rho, valid for |rho|<1, stationary, Gaussian; error is O(n^-2) and not uniform in rho (deteriorates near unit root). (ii) bias_mc = mean(rho_hat)-rho over R replications, MC SE = sd/sqrt(R). Meaningful under exact design: sigma=1, stationary y_1 ~ N(0, sigma^2/(1-rho^2)), intercept included, R=20000, seed 20261029 with numpy default_rng. 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. Also out/report.md (Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json, out/exclusions.csv, state files. Information rules. Only data/design.csv; follow design exactly; fresh series per replication. Invalidity. Missing/inconsistent design parameters, |rho|>=1 (stationary init undefined), different seed/R, wrong regression. Ambiguity noted. "n" in formula: design n=30 is the series length (29 regression obs). Use n=30 as the task specifies "at the design values"; sensitivity with n-1 reported in report only as a remark (computed by script).