1[2 {"id":"C1","text":"At n=30, rho=0.8 the OLS estimator of rho (with intercept) is biased downward by about 0.124 (MC SE 0.001).","results_keys":["bias_mc","bias_mc_se","rho_hat_mean"],"status":"supported","caveat":"Single design point, Gaussian innovations, stationary start."},3 {"id":"C2","text":"The first-order Marriott-Pope/Kendall approximation -(1+3rho)/n = -0.113 gets the sign and approximate size right (about 92% of the MC bias) but understates the bias by about 0.010.","results_keys":["bias_analytical","bias_mc"],"status":"supported","caveat":"The approximation is an O(1/n) expansion; it is not meant to be exact at a fixed n."},4 {"id":"C3","text":"The discrepancy between the MC bias and the approximation is statistically significant (about -9.9 MC standard errors), so it is not simulation noise. It is consistent with O(n^-2) remainder terms.","results_keys":["discrepancy_se_units","bias_mc_se"],"status":"supported","caveat":"The SE-unit magnitude grows with R. Attributing the gap to O(n^-2) terms is an interpretation; we did not test it by varying n."},5 {"id":"C4","text":"The Monte Carlo sampling sd of rho_hat (0.149) is larger than the textbook asymptotic SE sqrt((1-rho^2)/n) (0.110).","results_keys":["rho_hat_sd_mc","se_asymptotic"],"status":"supported","caveat":"Applies to this design only."}6]7