# 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 estimator rho_hat (regression on constant and y_{t-1}, t=2..n) in finite samples, and how well does the Marriott-Pope/Kendall first-order approximation -(1+3rho)/n describe it at the design (n=30, rho=0.8)?

Estimands. (i) bias_analytical = -(1+3rho)/n (deterministic). (ii) bias_mc = E[rho_hat]-rho, estimated by mean over R replications, with MC SE = sd/sqrt(R). Meaningful under: Gaussian iid innovations, |rho|<1, stationary start, intercept estimated. Also se_asymptotic = sqrt((1-rho^2)/n) as baseline scale.

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. out/report.md (sections Question; Data and exclusions; Method; Results; Uncertainty; Limitations and open issues), out/analysis.py, out/claims.json; plus protocol files (state/, exclusions.csv).

Information rules. Use only data/design.csv; follow design exactly (n, rho, sigma, intercept, stationary init, R, seed via numpy default_rng); c=0; fresh series per replication.

Invalidity. Design missing/inconsistent (e.g. |rho|>=1 with stationary init), not using the given seed/R, degenerate regressions.