1[2 {"id":"C1","text":"At n=30, rho=0.8 the OLS estimator of rho (with intercept) is biased downward by about 0.122 (MC SE 0.001).","results_keys":["bias_mc","bias_mc_se","rho_hat_mean"],"status":"supported","caveat":"Valid only for this design point (Gaussian, stationary start)."},3 {"id":"C2","text":"The Marriott-Pope/Kendall first-order approximation -(1+3rho)/n = -0.113 captures most (~93%) of the actual bias.","results_keys":["bias_analytical","bias_mc"],"status":"supported","caveat":"Uses n = series length 30; with n-1 the value is -0.117."},4 {"id":"C3","text":"The approximation understates the bias by about 0.009, a gap of 8.6 MC standard errors, consistent with the omitted O(n^-2) terms of a first-order expansion rather than MC noise.","results_keys":["discrepancy_se_units","bias_mc","bias_analytical","bias_mc_se"],"status":"supported","caveat":"Attribution to O(n^-2) terms is an interpretation; no higher-order expansion was computed."},5 {"id":"C4","text":"The bias is of the same order as the sampling variability: the MC sd of rho_hat (0.148) exceeds the asymptotic SE (0.110), and the bias is about 1.1 asymptotic SEs.","results_keys":["rho_hat_sd_mc","se_asymptotic","bias_mc"],"status":"supported","caveat":"Single design point."}6]7