Problems with the Asymptotic Theory of Maximum Likelihood Estimation in Integrated and Cointegrated Systems
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单整与协整系统中极大似然估计渐近理论的困难
- 研究问题
- 在参数非线性的单整与协整系统中，为何通常的一致性证明和得分 Taylor 展开可能失效，怎样建立估计量极限分布？
- 方法与思路
- 作者结合一致性、长期参数估计的收敛阶及标准化信息矩阵的随机等度连续条件，并用含单整和平稳变量的回归示范。
- 材料陈述的贡献
- 摘要称，文章扩展适用于参数非线性系统的随机等度连续结果，提出处理极限分布推导困难的路径及一致性验证方法。
- 阅读关注点
- 应核对长期参数所需的收敛阶、信息矩阵标准化方式与随机等度连续条件，以及示例中如何证明一致性并推广。
- 阅读边界
- 仅据所给 Crossref 摘要，不能断定所有非线性单整模型都适用；具体充分条件、证明细节和推广边界未说明。
原文摘要
Problems with the asymptotic theory of nonlinear maximum likelihood estimation in integrated and cointegrated systems are discussed in this paper. One problem is that standard proofs of consistency generally do not apply; another one is that, even if the consistency has been established, it can be difficult to deduce the limiting distribution of a maximum likelihood estimator from a conventional Taylor series expansion of the score vector. It is argued in this paper that the latter difficulty can generally be resolved if, in addition to consistency, an appropriate result of the order of consistency of the long-run parameter estimator of the model is available and the standardized sample information matrix satisfies a suitable extension of previous stochastic equicontinuity conditions. To make this idea applicable in particular cases, extensions of the author's recent stochastic equicontinuity results, relevant for many integrated and cointegrated systems with nonlinearities in parameters, are provided. As an illustration, a simple regression model with integrated and stationary regressors and nonlinearities in parameters is considered. In this model, the consistency and order of consistency of the long-run parameter estimator are obtained by employing extensions of well-known sufficient conditions for consistency. These conditions are applicable quite generally, and their verification in the special case of this paper suggests how to proceed in more complex models.