Functional Limit Theory in Econometrics

这个项目包括四个截然不同但相互关联的概率泛函极限理论研究领域。它们是：(1)参数不变性的最优检验，(2)非平稳时间序列的中值无偏估计和可信区间的构造，(3)相依非同分布随机变量的经验过程极限理论，(4)半参数计量经济学方法。这项研究的结果将为应用经济分析提供强大的新工具，包括研究全球环境变化的经济学。所提出的关于参数恒定性的工作包括未知变化点的结构变化测试和状态转换测试。该项目的这一部分很重要，因为当标准正则性条件失效时，目前还没有可用于测试参数不变性的渐近最优测试。由于目前的检验效率较低，因此本文提出的中值无偏估计和可信区间构造的研究具有重要意义。在这个项目下开发的新工具可以用来为分析人员提供更多关于经验经济学中经常遇到的时间序列问题类型的信息。相依非同分布随机变量的基本极限结果在各种时间序列计量经济学问题中也有应用。在第四个研究领域，该项目对半参数和非参数估计的异方差、自相关、渐近正态进行了检验。半参数估计被经济学家广泛使用，因为许多经济问题的数据不符合标准参数分析所需的假设，而这些新的检验可以用于非常广泛的半参数估计。这些方法特别适合于在全球变化经济学中遇到的预测和实证分析问题，因为数据质量很差，许多基本的经济关系存在不确定性，以及正在研究的经济体系结构可能发生变化。

This project encompasses four distinct, but interrelated areas of research in probabilistic functional limit theory. They are: (1) optimal tests of parameter constancy, (2) median unbiased estimation and confidence interval construction for nonstationary time series, (3) empirical process limit theory for dependent non-identically distributed random variables, and (4) semiparametric econometric methods. The results of this research will provide powerful, new tools for applied economic analysis including research on the economics of global environmental change. The proposed work on parameter constancy covers tests of structural change with an unknown change point and tests of regime switching. This part of the project is important because there currently are no asymptotically optimal tests available for testing for parameter constancy when the standard regularity conditions fail. The proposed research on median unbiased estimation and confidence interval construction is significant because current tests have low power. The new tools developed under this project can be used to provide analysts more information for the types of time series problems that are frequently encountered in empirical economics. The basic limit results for dependent non-identically distributed random variables also have applications in a wide variety of time series econometric problems. In the fourth area of research the project develops tests for heteroskedasticity, autocorrelation, asymptotic normality for semiparametric and nonparametric estimators. Semiparametric estimators are widely used by economists because the data for many economic problems do not fit the assumptions required for standard parametric analysis and these new tests can be used for a very wide range of semiparametric estimators. These methods are especially appropriate for the type of forecasting and empirical analytical problems encountered in the economics of global change because of the poor quality of the data, the uncertainty about many of the underlying economic relationships, and the possibility of changes in the structure of the economic system being studied.