Further Generalizations of Cointegration: Modeling Many Variables and Introducing Repellors

该项目对经济时间序列分析的统计理论做出了重要贡献。它代表了早期关于协整的工作的继续，协整是捕捉动态变量之间平衡关系的一种方式。一个向量时间序列XT称为协整的，如果XT的元素水平的线性组合是有限方差平稳的。许多宏观经济学的实证研究表明，经济时间序列数据通常包括非平稳过程，如趋势，因此从长期来看是相互联系的。为了对经济中变量的实际变动有任何有意义的洞察，必须消除非平稳过程的影响。协整是这样做的一种方式，因为时间序列变量水平的线性组合是稳定的，即使基础序列不是。在以前的工作中，线性组合是序列水平的吸引子。在这个项目中这些概念的扩展涉及到排斥体的概念，它是相空间中的一个区域，XT相对可能从该区域移动。负引力的概念是为驱避物而提出的。在确定性模型中，吸引子和排斥子都与稳定和不稳定的平衡有关，本项目的工作将对它们的存在进行统计检验。其目标是提供一套更通用的工具，通过吸引子和不同的吸引力强度来研究短期记忆经济过程，以及用排斥因素模拟包括趋势在内的长期记忆过程。该项目的第二部分涉及协整时间序列线性系统中的维度问题。将经济划分为多个部门，并估计和分析每个部门的共同向量。这将使分析的变量比所有系列都联合考虑时少得多。

This project makes an important contribution to the statistical theory of the analysis of economic time series. It represents a continuation of earlier work on cointegration, which is a way to capture equilibrium relations among dynamic variables. A vector time series xt is said to be cointegrated if a linear combination of the levels of the elements of xt is stationary with finite variance. Much empirical research in macroeconomics has shown that economic time series data typically include non-stationary processes such as trends and are therefore linked together in the long run. To gain any meaningful insight into the actual movements of the variable in the economy, they must be purged of the influence of the non-stationary processes. Cointegration is a way of doing this since the linear combinations of the levels of time series variables are stationary, even if the underlying series are not. In prior work, the linear combination is an attractor for the levels of the series. The extension of these concepts in this project involve the concept of a repellor, which is a region in the phase space, away from which xt is relatively likely to move. The concept of a negative strength of attraction is developed for a repellor. Both attractors and repellors are related to stable and unstable equilibria in deterministic models and the work in this project will develop statistical tests for their presence. The goal is to provide a more general set of tools for studying short memory economic processes, through attractors and varying strength of attraction; and for modelling long memory processes, including trends, with repellors. A second part of the project involves work on the dimensionality problems in linear systems of cointegrated time series. The economy is divided into sectors and a common vector of each sector is estimated and analyzed. This will allow for an analysis with many fewer variables than if all of the series are considered jointly.