Cointegration

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 x_t and y_t described by the following model:

where x_t is a non-stationary time series, u_t is a stationary time series. In this case, the time series y_t and x_t are cointegrated – because the time series

which is a linear combination of x_t and y_t, is a stationary time series ( u_t).