Cointegration

In econometrics, cointegration is a statistical property describing a long-term, stable relationship between two or more time series variables, even if those variables themselves are individually non-stationary (i.e., they have trends). This means that despite their individual fluctuations, the variables move together in the long run, anchored by an underlying equilibrium relationship.

More formally, if several time series are individually integrated of order d (meaning they require d differences to become stationary) but a linear combination of them is integrated of a lower order, then those time series are said to be cointegrated. That is, if (X,Y,Z) are each integrated of order d, and there exist coefficients a,b,c such that aX + bY + cZ is integrated of order less than d, then X, Y, and Z are cointegrated.

Cointegration is a crucial concept in time series analysis, particularly when dealing with variables that exhibit trends, such as macroeconomic data. In an influential paper,^[1] Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends.