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具有分数单整误差的协整时间序列渐近推断AI 解读

Vector valued autoregressive models with fractionally integrated errors are considered. The possibility of the coefficient matrix of the model having eigenvalues with absolute values equal or close to unity is included. Quadratic approximation to the log-likelihood ratios in the vicinity of auxiliary estimators of the parameters is obtained and used to make a rough identification of the approximate unit eigenvalues, including complex ones, together with their multiplicities.…

线性协整时间序列系统中的渐近推断AI 解读

This paper considers vector-valued nonstationary time series models, in particular, autoregressive models, whose nonstationarity is driven by a few nonstationary (induced by “unit roots”) trends, in such a way that some of the linear combinations of the components of the vector model will be stationary. Models of this form are called cointegrated models. These stationary linear combinations are called cointegrating relationships. Asymptotic inference problems associated with…

渐近理论的若干方面及其在时间序列模型中的应用AI 解读

The primary purpose of this paper is to review a very few results on some basic elements of large sample theory in a restricted structural framework, as described in detail in the recent book by LeCam and Yang (1990, Asymptotics in Statistics: Some Basic Concepts . New York: Springer), and to illustrate how the asymptotic inference problems associated with a wide variety of time series regression models fit into such a structural framework. The models illustrated include…

特征根位于或接近单位圆的自回归最小二乘估计量的渐近行为AI 解读

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…

线性随机模型估计量分布的强近似：平稳与爆炸性 AR 模型AI 解读

It is shown that in the stationary autoregressive case (Part I [Sections 1-5)] the distributions of least squares estimators and their close relatives such as sample autocovariances and the recently introduced general $M$-estimators converge to suitable Gaussian distributions uniformly over all Borel sets and uniformly over suitable neighborhoods of the parameter. Specifically, the notion of strongly asymptotically shift equivariance is introduced and it is shown that the…

估计量分布的强收敛AI 解读

It is shown that the convergence in law of estimators entails convergence uniformly over all Borel sets whenever the estimators are asymptotically equivariant in a suitable sense and the likelihood ratios of the sample are appropriately smooth. This result generalizes a recent result of Boos in many directions.