Some Aspects of Asymptotic Theory with Applications to Time Series Models
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 ↓
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分类依据与纠错
AI 根据所提供的论文材料归类：摘要明确涉及单位根、协整等时间序列模型，并以 ARCH 波动率模型为非线性例子。
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渐近理论的若干方面及其在时间序列模型中的应用
- 研究问题
- 如何把协整、单位根和 ARCH 等时间序列模型的渐近推断纳入统一结构框架，并处理非高斯误差与自适应估计？
- 方法与思路
- 作者回顾大样本理论的部分基础结果，利用似然比的近似二次结构和辅助参数估计，说明多类时间序列模型的推断。
- 材料陈述的贡献
- 摘要称，该框架可在误差密度的 Fisher 信息有限且非奇异等条件下使用，非高斯情形的推断可归结为类似高斯的结构。
- 阅读关注点
- 应核对各模型对应的似然比近似、辅助估计要求，以及估计误差密度的条件和统一框架在不同模型间的适用边界。
- 阅读边界
- 仅据所给 Crossref 摘要，不能把统一框架理解为无需额外条件；具体模型的假设、实现和其他版本变化均未完整说明。
原文摘要
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 many linear time series models, including cointegrated models and autoregressive models with unit roots that are of wide current interest. The general treatment also includes nonlinear models, including what have become known as ARCH models. The possibility of replacing the density of the error variables of such models by an estimate of it (adaptive estimation) based on the observations is also considered. Under the framework in which the asymptotic problems are treated, only the approximating structure of the likelihood ratios of the observations, together with auxiliary estimates of the parameters, will be required. Such approximating structures are available under quite general assumptions, such as that the Fisher information of the common density of the error variables is finite and nonsingular, and the more specific assumptions, such as Gaussianity, are not required. In addition, the construction and the form of inference procedures will not involve any additional complications in the non-Gaussian situations because the approximating quadratic structure actually will reduce the problems to the situations similar to those involved in the Gaussian cases.