Cointegration is a statistical tool for describing the co-movement of data measured over time. The concept of cointegration is widely used in applied time series analysis, especially in econometrics.
Two (or a greater number) of nonstationary time series are called to be cointegrated if there exists a stationary linear combination of these variables. Consider, for example, two time series xt and yt described by the following model:
where xt is a non-stationary time series, ut is a stationary time series. In this case, the time series yt and xt are cointegrated - because the time series
which is a linear combination of xt and yt , is a stationary time series ( ut ).