On the Asymptotic Behavior of Least-Squares Estimators in AR Time Series with Roots Near the Unit Circle
研究了当自回归模型的特征多项式根在单位圆上或附近时，最小二乘估计量的渐近性质，包括收敛到布朗运动泛函的分布，并强化为一致收敛。
Some asymptotic properties of the least-squares estimator of the parameters of an AR model of order p, p ≥ 1, are studied when the roots of the characteristic polynomial of the given AR model are on or near the unit circle. Specifically, the convergence in distribution is established and the corresponding limiting random variables are represented in terms of functionals of suitable Brownian motions. Further, the preceding convergence in distribution is strengthened to that of convergence uniformly over all Borel subsets. It is indicated that the method employed for this purpose has the potential of being applicable in the wider context of obtaining suitable asymptotic expansions of the distributions of leastsquares estimators.