Higher-Order Asymptotic Expansions of the Least-Squares Estimation Bias in First-Order Dynamic Regression Models.

An approximation to order T-2 is obtained for the bias of the least-squares estimator in the stationary ARX model which yields generalisations of Kendall's and White's classic results for particular variants of AR(1) models. The results show that generally the second-order approximation is considerably better than its first-order counterpart in ARX models. This is also largely true for AR(1) models except that in such models second-order approximations may be vulnerable in the near unit root case.