1[2 {"id":"C1","text":"The Monte Carlo finite-sample bias of the OLS AR(1) slope at n=30, rho=0.8 is about -0.124 with MC SE about 0.001.","results_keys":["bias_mc","bias_mc_se","rho_hat_mean","n_analysed"],"status":"supported","caveat":"Single design point; Monte Carlo error only."},3 {"id":"C2","text":"The first-order Marriott-Pope/Kendall approximation gives -0.113 and understates the magnitude of the bias by about 8%, a gap of about 9.9 MC standard errors.","results_keys":["bias_analytical","discrepancy_se_units","supp_relative_error_analytical"],"status":"supported","caveat":"With n-1=29 in the formula the gap is about 6.1 SE (supp_discrepancy_se_units_n_minus_1); still significant."},4 {"id":"C3","text":"The discrepancy is consistent with the formula being a leading-order O(1/n) approximation that has an O(n^-2) remainder; it does not show the formula is invalid asymptotically.","results_keys":["bias_analytical","bias_mc","discrepancy_se_units"],"status":"supported","caveat":"Interpretation relies on asymptotic theory; the MC evaluates one design point and cannot verify rates."},5 {"id":"C4","text":"The sampling sd of rho_hat (0.149) exceeds the textbook asymptotic SE (0.110) by about 36%, and the bias is about 0.83 of the sd.","results_keys":["rho_hat_sd_mc","se_asymptotic","supp_sd_ratio_mc_to_asymptotic"],"status":"supported","caveat":"Design-specific."}6]7