What is "cointegration"

n. (context mathematics English) The condition of two non-stationary time series whose linear combination is stationary

Cointegration is a statistical property of a collection (X1,X2,...,Xk) of time series variables. First, all of the series must be integrated of order 1 (see Order of Integration). Next, if a linear combination of this collection is integrated of order zero, then the collection is said to be co-integrated. Formally, if (X,Y,Z) are each integrated of order 1, and there exist coefficients a,b,c such that aX+bY+cZ is integrated of order 0, then X,Y, and Z are cointegrated. Cointegration has become an important property in contemporary time series analysis. Time series often have trends — either deterministic or stochastic. In an influential paper, Charles Nelson and Charles Plosser (1982) provided statistical evidence that many US macroeconomic time series (like GNP, wages, employment, etc.) have stochastic trends — these are also called unit root processes, or processes integrated of order 1 — I(1). They also showed that unit root processes have non-standard statistical properties, so that conventional econometric theory methods do not apply to them.