条件独立性及其相关假设：基于特征函数的计量检验和实证研究

Conditional independence is a widely used assumption in economic and financial modeling. It encompasses many important hypotheses in econometrics and statistics, such as Granger causality, missing at random, markov property, and plays an important role in econometric theories and empirical applications. This project, mainly based on the nonparametric estimation and characteristic function, will propose several tests for conditional independence and its related assumptions, and further apply the theoretical results to economic and financial analysis. Firstly, a unified framework will be proposed to test conditional independence and gauge possible sources of conditional dependence. Secondly, a series of tests will be introduced to test some key hypotheses including missing at random, Granger causality in distribution, strict stationarity and exogeneity. Thirdly, the proposed test statistics will be applied to check the reliability of some basic assumptions in the related literature. Moreover, the validity of classical models will be revisited, while some new models and their estimates will be introduced. Finally, this project will empirically study the interactive and predictive relationships between China’s economic and financial variables in nonlinear framework, including predictability of key economic and financial variables, Granger causalities between macroeconomic variables, spillover effect of financial market, missing at random of microeconomic data. The proposed research will not only contribute to the development of econometric testing, but also provide reasonable tools for empirical applications and further derive reliable conclusions and policy recommendations.

条件独立性不仅在经济金融建模中得到了广泛应用，而且还囊括了格兰杰因果关系、随机缺失、马尔科夫性质等一系列重要的计量假设，在计量理论和实证应用中发挥着重要作用。本研究将基于非参数估计和特征函数，构造条件独立性及其相关假设的检验统计量，并将其应用到经济金融分析中。具体研究内容包括：一是提出更优的条件独立性检验统计量，并且在统一框架下识别变量的具体条件相依形式；二是构造随机缺失、依分布格兰杰因果关系、严平稳、外生性等计量假设的检验统计量；三是借助这些统计量考察相关文献基本假设成立与否，从而重新审视其研究结论的可靠性，并尝试开发新的模型与估计方法；四是在非线性框架下实证探讨我国经济金融变量的影响和预测关系，包括经济金融指标可预测性、经济变量格兰杰因果关系、金融市场溢出效应、微观数据随机缺失等。本研究不仅有助于推动相关计量检验方法的发展，而且有助于构建恰当的实证模型，得到可靠的分析结论和政策建议。

条件独立性不仅在经济金融建模中得到了广泛应用，而且还囊括了格兰杰因果关系、随机缺失、马尔科夫性质等一系列重要的计量假设，在计量理论和实证应用中发挥着重要作用。本研究将非参数估计与特征函数结合，构造了条件独立性检验统计量，对其拓展构造了严平稳、遗漏变量、条件异方差等假设的检验统计量，并且进一步将理论研究成果应用到实证分析中。具体研究内容包括：一是提出了具有更快收敛速度、更优有限样本性质的条件独立性检验统计量，并且构造了一系列派生统计量，包括遗漏变量检验、条件异方差检验等；二是构造了严平稳、弱平稳、p阶平稳等计量假设的检验统计量；三是将相关研究思想应用到因子模型和面板数据模型中，提出了时变因子模型和异质时变面板数据模型，并且提出了因子模型时变特征的检验统计量；四是在非线性框架下实证探讨我国经济金融变量的影响关系，包括我国经济周期和金融周期的度量和联动性研究、金融市场风险传染效应研究、我国货币政策的非线性特征等。本研究不仅推动了相关计量检验方法的发展，而且为实证分析人员提供了恰当的计量工具，有助于构建恰当的实证模型，得到可靠的分析结论和政策建议。