Introductory Mathematics and Statistics for Islamic Finance, + Website

Chapter 18Co-Integration: Theory and Applications

Variables such as gross domestic product, investment, and consumption have close relations in the long-run; however, they may deviate from each other in the short-run. Likewise, stock prices and dividends of the issuing enterprise are closely related in the long-run; however, in the short-run, they may wander from each other. We may multiply the examples of long-run relationships between economic variables such as the level of education and the level of development in an economy, or the degree of machinery use and agriculture production. When we deal with two integrated processes, for example, of order , and, it is useful to distinguish short-run relationships from long-run relationships. The former relates to links that do not persist. The long-run relationships are closely associated with concepts of equilibrium in economic theory and persistence of co-movements of economic time series.

An examination of economic or financial relationships between time series will lead to discuss aspects of time series analysis, co-integration, and error-correction. The first step is to clarify the statistical notion of stationarity and its links to the concept of equilibrium. We say that an equilibrium relationship holds between two variables, and if the error by which actual observations deviate from this equilibrium is a mean-stationary process. ...