IDENTIFICATION OF COVARIANCE STRUCTURES
协方差结构的识别AI 解读 ↓
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协方差结构的识别
- 研究问题
- 能否仅凭约束而不依赖待估真实参数判断协方差结构的识别，并使大规模结构模型的识别检查自动化？
- 方法与思路
- 作者建立依赖约束的识别充要条件，并提出结构条件，以约束矩阵构造的矩阵可逆性配合阶条件判断识别。
- 材料陈述的贡献
- 摘要称给出不依赖参数估计的识别充要条件；另有结构条件与阶条件联合构成充分条件，使软件自动检查可行。
- 阅读关注点
- 核对充要条件与联合充分条件的区别、约束矩阵的构造及可逆性要求，并查看在结构 VAR 中的实际检查步骤。
- 阅读边界
- 仅据所给出版社摘要，无法写出判据矩阵或确认适用约束类型；摘要未说明局部与全局识别的具体区分。
原文摘要
The issue of identification of covariance structures, which arises in a number of different contexts, has been so far linked to conditions on the true parameters to be estimated. In this paper, this limitation is removed.As done by Johansen (1995, Journal of Econometrics 69, 112–132) in the context of linear models, the present paper provides necessary and sufficient conditions for the identification of a covariance structure that depends only on the constraints and can therefore be checked independently of estimated parameters.A structure condition is developed, which only depends on the structure of the constraints. It is shown that this condition, if coupled with the familiar order condition, provides a sufficient condition for identification. In practice, because the structure condition holds if and only if a certain matrix, constructed from the constraint matrices, is invertible, automatic software checking for identification is feasible even for large-scale systems.Most of the paper focuses on structural vector autoregressions, but extensions to other statistical models are also briefly discussed.I thank all the participants at the meeting held in Pavia on June 11, 2004, in honor of Carlo Giannini for their comments; it goes without saying that Carlo himself provided not only acute observations on the day but also the main inspiration for this piece of work. Sadly, Carlo passed away on September 11, 2004, and this paper is dedicated to his memory. Pär Österholm spotted several mistakes in an earlier version and helped me clarify some implementation details. Thanks are also due to Gianni Amisano, Bruce Hansen, Giulio Palomba, Paolo Paruolo, and two anonymous referees. The usual disclaimer obviously applies.