Synchronization and Other Generalizations of Cointegration

这个项目的主要部分是关于低频下协整过程的相对动力学的一个新概念，称为同步。当一个经济体的长期组成部分密切相关，并导致重要的经济变量同时同步变动时，就会发生同步。该项目的目标是：(1)发展一种简单的宏观经济理论，这将导致某种形式的同步；(2)设计协整系列的同步测试；(3)开发非协整系列的同步测试；(4)寻找一种适当的不均衡机制，以实现同步协整作为均衡；(5)将发展到各种实际序列的技术应用于各种实际序列，包括不同期限的利率、一国不同部门的就业率以及加拿大和美国等贸易流动强劲国家的人均国民生产总值；以及(6)对工程学和物理学中有关同步的文献进行调查，看看这些文献是否与经济学相关或适用于经济学。该项目还分析了具有时变参数的协整。这是一项非常令人兴奋和重要的研究。这位研究人员的早期工作开发了一种称为协整的时间序列的统计特征，其中独立非平稳的数据序列的线性组合是平稳的。这一发展非常重要，因为大多数经济时间序列数据通常包括非平稳过程，如趋势。要对经济中变量的实际变动有任何有意义的洞察，就必须清除数据中非平稳过程的影响。协整检验和技术极大地简化了实现平稳性的过程，特别是对于包括几个数据序列的分析模型而言，每个数据序列都包含相似的增长趋势。同步，这个项目的主题，开辟了协整研究的新途径。可以证明，经济均衡意味着关键经济变量的同步。因此，该项目开发的同步性检验将为经济学家提供新的、更有力的检验，以检验经济均衡的存在和特征。

The main part of this project is concerned with a new idea about the relative dynamics of co-integrated processes at low frequencies called synchronization. Synchronization occurs when long-run components of an economy are closely related and cause important economic variables to move together in phase. The objectives of the project are (1) to develop a simple macroeconomic theory which would lead to some form of synchronization; (2) to devise tests of synchronization for co- integrated series; (3) to develop tests of synchronization for series that are not co-integrated; (4) to find an appropriate disequilibrium mechanism that leads to synchronized co- integration as an equilibrium; (5) to apply the techniques developed to various actual series, including interest rates of differing maturities, employment rates in different sectors of a country and GNP per capita for a pair of countries with strong trade flows such as Canada and the United States; and (6) to survey the literature on synchronization in engineering and physics to see if this literature is relevant or applicable to economics. The project also analyzes co-integration with time- varying parameters. This is very exciting and important research. Earlier work by the investigator developed a statistical characterization of time series known as co-integration in which a linear combination of data series that are independently non-stationary is stationary. This development is extremely important because most economic time series data typically include non-stationary processes such as trends. To gain any meaningful insight into actual movements of the variables in an economy, one must purge the data of the influence of non-stationary processes. Co-integration tests and techniques have greatly simplified achieving stationarity especially for analytical models including several data series each containing similar growth tendencies. Synchronization, the subject of this project, opens a new line of research within co- integration. Economic equilibrium can be shown to imply synchronization of key economic variables. Thus the tests for synchronization developed by this project will give economists new and more powerful tests for the existence and characteristics of economic equilibria.