Cointegration

Cointegration is an econometric technique for testing the correlation between non-stationary time series variables. For instance, a company's stock price and its dividend yield move through time, each roughly following a random walk. Testing the hypothesis that there is a statistically significant connection between the yield and the price could now be done by finding a cointegrating vector. (If such a vector has a low order of integration it can signify an equilibrium relationship between the original series, which are said to be cointegrated of an order below one.)

Before the 1980s many economists used linear regressions on (de-trended) non-stationary time series data, which Clive Granger and others showed to be a dangerous approach, that could produce spurious correlations. His 1987 paper with Robert Engle, Co-integration and error correction: Representation, estimation and testing”, (Econometrica 55) formalized the cointegrating vector approach, and coined the term, although the hyphen is no longer used. For his contribution to the technique's development Clive Granger shared the 2003 Nobel Memorial Prize.

It is often said that cointegration is a means of valid hypothesis testing between two variables having unit roots (Integrated of order one). In practise, this is how it tends to be used in typical econometric tests, but cointegration is more generally applicable and can be used for variables Integrated of higer order (to detect correlated accelerations or other second differencing effects). Multicointegration extends the cointegration technique beyond two variables, and occasionally to variables Integrated at different orders.