What is Cointegration, cointegrating vector, cointegration rank?

The components of a vector of unit-root processes are cointegrated (cointegration) if some linear combination $\beta^\top Y_t$ is stationary; $\beta$ is a cointegrating vector. The number of linearly independent cointegrating vectors is the cointegration rank $r$, and $k - r$ is the number of common stochastic trends.