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.
