Mildly Explosive Time Series and Economic Bubbles

这项拟议的研究试图将目前的单位根和协整计量方法扩展到适度整合和适度爆炸性的数据。这样的时间序列是由Pi和Tassos Magdalinos在最近的工作中引入的，其根源属于更大的团结社区，而不是传统的本地对团结的根源。新的框架包括经常发生的具有根的实际案例，如Rho=0.95，并有助于弥合渐近理论中平稳、局部到统一和爆炸模型之间的不连续性。该项目将建立在这些想法的基础上，开发具有适度集成和适度爆炸性回归变量的多元回归的极限理论，并启动一个相关的经验应用程序。特别是，这项研究将提供一个框架，用于推广标准的协整回归，并将这些回归与带有平稳回归变量的联立方程模型联系起来。当回归变量接近积分时，传统的估计协整回归的方法甚至不能产生渐近有效的推断过程，并且在计量经济学检验中可能会发生严重的大小扭曲。新的框架将提供一种通用的推理方法来解决这一困难，并允许在回归变量中进行温和的积分，使其适用于一般实际应用。轻微的爆炸性回归也提供了有趣的新可能性，包括使用中心极限论点。该项目将探索多变量系统，并在广泛的弱依赖创新、分布和初始条件下通过不变原理验证测试程序。这些程序将有助于处理经历金融泡沫等极端行为时期的经济数据，以及存在体现跨变量污染影响的爆炸性协整回归的情况。还将分析周期性泡沫破裂的模型，对具有更现实样本路径性质的现有模型进行一些扩展，并开发在存在泡沫的情况下进行计量经济学测试和推断的程序。广泛影响：经济变量的极端变动可能会产生广泛的社会经济影响，导致个人财富和金融安全的波动，资本配置不当，并威胁经济机构的信誉。这些方法将有助于我们通过开发新的经济泡沫模型、检测泡沫活动的新方法以及在存在爆炸行为时进行统计推断和估计变量间污染的新程序，来帮助我们理解这些经济问题。该项目的学术价值在于，它对适度整合和轻微爆炸性数据的分析做出了科学贡献，它将协整方法扩展到涵盖这些数据，以及它对经济和金融泡沫研究的经验贡献。调查员将通过在这些主题上的联合和指导工作来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.