ASYMPTOTIC EFFICIENCY OF THE ORDINARY LEAST SQUARES ESTIMATOR FOR REGRESSIONS WITH UNSTABLE REGRESSORS
研究了当回归元具有单位根且误差平稳独立时，普通最小二乘估计量（OLSE）与广义最小二乘估计量（GLSE）渐近等价的充分条件，关键条件是回归元过程特征根的一个重数严格大于其他根的重数。
For regression models with general unstable regressors having characteristic roots on the unit circle and general stationary errors independent of the regressors, sufficient conditions are investigated under which the ordinary least squares estimator (OLSE) is asymptotically efficient in that it has the same limiting distribution as the generalized least squares estimator (GLSE) under the same normalization. A key condition for the asymptotic efficiency of the OLSE is that one multiplicity of a characteristic root of the regressor process is strictly greater than the multiplicities of the other roots. Under this condition, the covariance matrix Γ of the errors and the regressor matrix X are shown to satisfy a relationship (Γ X = XC + V for some matrix C ) for V asymptotically dominated by X , which is analogous to the condition (Γ X = XC for some matrix C ) for numerical equivalence of the OLSE and the GLSE.