Functional Limit Theory in Econometrics

本项目包含概率泛函极限理论中四个不同但相互关联的研究领域。它们是：(1)参数常数的最优检验；(2)非平稳时间序列的中位数无偏估计和置信区间的构造；(3)非同分布随机变量的经验过程极限理论；(4)半参数计量方法。这项研究的结果将为包括全球环境变化经济学研究在内的应用经济分析提供强有力的新工具。所提出的参数恒常性的研究工作包括带未知变化点的结构变化试验和状态切换试验。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恒常性的渐近最优测试。由于目前的测试功耗较低，对中值无偏估计和置信区间构建的研究具有重要意义。本项目下开发的新工具可用于为实证经济学中经常遇到的时间序列问题类型的分析师提供更多信息。相关非同分布随机变量的基本极限结果在各种时间序列计量问题中也有广泛的应用。在研究的第四个领域，该项目开发了半参数和非参数估计的异方差、自相关、渐近正态性的检验。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，这些新的检验可以用于非常广泛的半参数估计。这些方法特别适用于全球变化经济学中遇到的预测和经验分析问题，因为数据质量差，许多基本经济关系的不确定性，以及所研究的经济系统结构变化的可能性。

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.