1[2 {"id":"C1","text":"At n=30, rho=0.8 the OLS estimator of rho is downward biased; the Monte Carlo bias is about -0.122 with MC SE about 0.001.","results_keys":["bias_mc","bias_mc_se","rho_hat_mean","bias_mc_ci95"],"status":"supported","caveat":"Single design point; fixed seed."},3 {"id":"C2","text":"The Marriott-Pope/Kendall approximation -(1+3rho)/n = -0.113 captures the sign and roughly 93% of the magnitude of the bias (MC bias is ~8% larger).","results_keys":["bias_analytical","bias_mc","bias_ratio_mc_to_analytical"],"status":"supported","caveat":"Evaluated with n = series length 30; with n-1=29 the formula gives -0.117."},4 {"id":"C3","text":"The discrepancy between MC and analytical bias is statistically significant (-8.6 MC SEs; -4.9 with n-1), consistent with an O(1/n^2) remainder of a first-order approximation rather than a failure of it.","results_keys":["discrepancy_se_units","discrepancy_se_units_neff","bias_mc_se"],"status":"supported","caveat":"Attribution to higher-order terms is interpretive; the MC does not estimate those terms separately."},5 {"id":"C4","text":"The finite-sample bias exceeds the textbook asymptotic SE, and the MC sd of rho_hat is about 1.35 times the asymptotic SE.","results_keys":["bias_mc","se_asymptotic","rho_hat_sd_mc","sd_ratio_mc_to_asymptotic"],"status":"supported","caveat":"Specific to this design."},6 {"id":"C5","text":"The MC evidence does not establish the accuracy of the approximation at other (n, rho), error distributions or initial conditions.","results_keys":["design_n","design_rho"],"status":"not_evaluated","caveat":"Scope statement; only one design point was simulated."}7]8