Synchronization and Other Generalizations of Cointegration

这个项目的主要部分是关于在低频率下称为同步的协整过程的相对动力学的一个新想法。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步运动时，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)设计协整序列的同步检验；(3)对非协整序列进行同步检验；(4)寻找适当的非均衡机制，使同步协整成为均衡；(5)将所开发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的两个国家的人均国民生产总值；(6)对工程和物理学中关于同步的文献进行综述，看看这些文献是否与经济学相关或适用。该项目还分析了时变参数的协整。这是非常令人兴奋和重要的研究。研究者早期的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。这一发展是极其重要的，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。为了对经济中变量的实际运动有任何有意义的洞察，必须清除非平稳过程对数据的影响。协整检验和技术大大简化了平稳性的实现，特别是对于包含多个数据序列的分析模型，每个数据序列都包含类似的增长趋势。同步，这个项目的主题，在协整的研究中开辟了一条新的路线。经济均衡可以被证明意味着关键经济变量的同步。因此，本项目开发的同步性检验将为经济学家提供新的、更有力的检验经济均衡的存在和特征的方法。

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.