Mildly Explosive Time Series and Economic Bubbles

拟议的研究旨在扩大目前的计量经济学方法的单位根和协整，温和的综合和温和的爆炸性数据。这种时间序列在PI和Tassos Magdalinos最近的工作中引入，并且具有属于比传统的局部到单位根更大的单位邻域的根。新的框架包括经常发生的实际情况下，根，如ρ = 0.95，并有助于弥合不连续性的渐近理论之间的平稳，局部团结和爆炸模型。该项目将建立在这些想法的基础上，开发一个极限理论的多元回归与轻度集成和轻度爆炸回归，并启动相关的经验应用程序。特别是，该研究将提供一个框架，推广标准协整回归，并将这些回归与平稳回归的联立方程模型。 传统的方法估计协整回归甚至不能产生渐近有效的推理程序时，回归几乎是一体的，并在计量经济学测试中可能会发生相当大的规模失真。新的框架将使一般的推理方法，解决了这个困难，并允许温和的整合回归，使其适合一般的实际应用。温和的爆炸回归也提供了有趣的新的可能性，包括使用中心极限参数。该项目将探索多变量系统，并在广泛的弱相关新息，分布和初始条件下通过不变性原理验证测试程序。这些程序将是有用的，在处理经济数据，经历了极端的行为，如金融泡沫时期，并有爆炸性的协整回归体现跨变量的污染效应的情况下。还将分析周期性崩溃的泡沫模型，将提供对现有模型的一些扩展，使其具有更真实的样本路径特性，并将开发在泡沫存在的情况下进行计量经济学检验和推断的程序。经济变量的极端变动会产生广泛的社会经济影响，造成个人财富和金融安全的波动，资本分配不当，并威胁到经济机构的信誉。这些方法将通过开发经济泡沫的新模型、检测泡沫活动的新方法以及在存在爆炸性行为的情况下进行统计推断和估计变量污染的新程序，有助于我们对这些经济问题的理解。该项目的智力价值在于其对温和整合和温和爆炸性数据分析的科学贡献，其协整方法的扩展以涵盖此类数据，以及其对经济和金融泡沫研究的实证贡献。调查员将通过对这些主题的联合和指导工作，协助经济学研究生的研究培训。

The proposed research seeks to extend present econometric methodology of unit roots and cointegration to mildly integrated and mildly explosive data. Such time series were introduced in recent work by the PI and Tassos Magdalinos and have roots that belong to larger neighborhoods of unity than conventional local to unity roots. The new framework includes commonly occuring practical cases with roots such as rho = 0.95 and helps to bridge discontinuities in the asymptotic theory between stationary, local to unity and explosive models. The project will build on these ideas, develop a limit theory for multivariate regression with mildly integrated and mildly explosive regressors, and initiate a program of related empirical applications. In particular, the research will provide a framework for generalizing standard cointegrating regressions and for linking these regressions to simultaneous equations models with stationary regressors. Conventional approaches to estimating cointegrating regressions fail to produce even asymptotically valid inference procedures when the regressors are nearly integrated, and substantial size distortions can occur in econometric testing. The new framework will enable a general approach to inference that resolves this difficulty and permits mild integration in the regressors, making it suitable for general practical application.Mildly explosive regressions also offer intriguing new possibilities, including the use of central limit arguments. The project will explore multivariate systems and validate test procedures by invariance principles under a wide range of weakly dependent innovations, distributions, and initial conditions. These procedures will be useful in dealing with economic data that undergo periods of extreme behavior like financial bubbles, and cases where there are explosively cointegrated regressors embodying contamination effects across variables. Models of periodically collapsing bubbles will also be analyzed, some extensions to existing models that have more realistic sample path properties will be provided, and procedures for econometric testing and inference in the presence of bubbles will be developed.Broader Impact: Extreme movements in economic variables can have a wide socio-economic impact, producing swings in individual wealth and financial security, misallocating capital, and threatening the credibility of economic institutions. The methods will contribute to our understanding of these economic issues by developing new models of economic bubbles, new ways of detecting bubble activity, and new procedures for statistical inference in the presence of explosive behavior and for estimating contamination across variables. The project's intellectual merit is in its scientific contribution to the analysis of mildly integrated and mildly explosive data, its extension of cointegration methodology to cover such data, and its empirical contribution to the study of economic and financial bubbles. The investigator will assist the research training of graduate students of economics through joint and directed work on these topics.