The study of equilibrium relationships is at the heart of time series analysis. Because cointegration provides one way to study equilibrium relationships, it is a cornerstone of current time series analysis. The original idea behind cointegraton is that two series may be in equilibrium in the long run, but in the short run the two series deviate from that equilibrium. Clarke, Stewart, and Whiteley (1998, 562) explain that “cointegrated series are in a dynamic equilibrium in the sense that they tend to move together in the long run. Shocks that persist over a single period are ‘reequilibrated’ or adjusted by this cointegrating relationship.” Thus cointegration suggests a long-run relationship between two or more series that may move in quite different ways in the short run. Put a bit more formally, cointegration says that a specific combination of two non stationary series may be stationary. We then say these two series or variables are cointegrated, and the vector that defines the stationary linear combination is called the cointegrating vector.
Recall from the previous chapter that a time series is stationary when its mean and variance do not vary over or depend on time. Lin and Brannigan(2003, 153) point out that “many times series variables in the social sciences and historical studies are nonstationary since the variables typically measure the changing properties of social events over, for example, the last century or over the last x-number of months or days of observations. These variables display time varying means, variances, and sometimes autocovariances.”