Statistical methods for causality analysis and non-regular inference problems

在这个项目中，我打算从事与经济和金融中有用的模型的统计推断相关的广泛主题的研究。******考虑的主题包括以下几个：******静态和非动态模型的因果关系分析，以区分总影响、直接影响和间接影响，以及短期影响和长期影响。缺失解释变量模型的推理***C。对于通常的渐近分布理论不适用的各种“非规则”问题的推理，包括识别或通常的秩假设可能失败的问题。财务数据中的波动性分析。***E。存在序列依赖的拟合优度检验。******将使用有限样本和渐近方法，重点是界方法和基于模拟的推理。***从观察到的数据推断“因果关系”是许多统计研究中的一个中心问题，特别是如果结果旨在用于决策。与实验研究相比，当数据来自观察性研究时，这个问题可能相当具有挑战性，因为解释变量之间的相互作用无法控制。事实上，这种困难在经济和金融数据中很常见，但在使用非实验数据的其他领域（如社会学、流行病学）也很常见。“反馈”和延迟效应可能存在，在得出结论时应予以考虑。特别重要的是要区分直接、间接和全面的影响。***我打算在静态和动态模型的背景下对这些问题进行研究。对于非动态设置，将考虑回归和联立方程模型。在回归的情况下，考虑到测试和测量直接、间接和总影响，一般目标是允许解释变量之间的相互作用。这项工作将涉及发展正式的数学概念和有关的统计理论，以分析总的、直接的和间接的影响。为此目的，我认为，研究与缺失或误测解释变量的回归推理构成了一个有用的中间统计问题。在这种情况下，将提出有限样本界和渐近界。这种方法也将用于计量经济学中流行的线性和非线性结构方程模型。***时间序列数据提供了动态相互作用以及时间延迟的信息。在宏观经济和金融中广泛使用的动态模型中，不同视界的因果关系概念（Dufour和Renault， 1998, Econometrica）将以测量直接和间接“脉冲响应系数”的观点进行扩展。线性多元时间序列模型和非线性时间序列模型都将被考虑。*****

In this program, I intend to pursue research on a wide array of topics relevant to statistical inference for models useful in economics and finance.******The topics considered include the following ones.******A. Causality analysis in both static and non-dynamic models, with the view of distinguishing between total, direct and indirect effects, as well short-run and long-run effects.***B. Inference on models with missing explanatory variables***C. Inference for various “non-regular” problems, where usual asymptotic distributional theory is not applicable, including problems where identification or usual rank assumptions may fail.***D. Volatility analysis in financial data.***E. Goodness-of-fit tests in the presence of serial dependence.******From finite-sample and asymptotic methods will be used, with an emphasis on bound approaches and simulation-based inference.***Inference on “causality” from observed data is a central issue in many statistical studies, especially if the results are meant to be used for decision making. This problem can be quite challenging when data come from observational studies, in contrast with experimental studies, because interactions between explanatory variables cannot be controlled. Indeed, this difficulty is common in economic and financial data, but also in other areas where non-experimental data are used (e.g., sociology, epidemiology). “Feedbacks” and delayed effects may be present and should be taken into account when drawing conclusions. In particular, it is important to distinguish between direct, indirect and total effects. ***I intend to pursue research on these problems in the context of both static and dynamic models. For non-dynamic setups, both regression and simultaneous equation models will be considered. In the regression case, the general objective consists in allowing for interaction between explanatory variables, in view of testing and measuring direct, indirect and total effects. This work will involve developing both formal mathematical concepts and the relevant statistical theory, to analyze total, direct and indirect effects. For this purpose, I argue that studying inference on regression with missing or mismeasured explanatory variables constitute a useful intermediate statistical problem. Both finite-sample and asymptotic bounds will be proposed in this context. This approach will also be carried to linear and nonlinear structural equation models, popular in econometrics. ***Time series data provide information on dynamic interactions along with time delays. In dynamic models, which are widely used in macroeconomics and finance, the notion of causality at different horizons (Dufour and Renault, 1998, Econometrica) will be extended with the view of measuring direct and indirect “impulse response coefficients”. Both linear multivariate time series models and nonlinear ones will be considered.*****