Vector error-correction model क्या है?

A vector error-correction model writes a VAR in differences plus a levels term, $\Delta Y_t = \alpha\beta^\top Y_{t-1} + \sum_{i=1}^{p-1}\Gamma_i\Delta Y_{t-i} + \mu + \varepsilon_t$, with $\alpha$ and $\beta$ of dimension $k \times r$: $\beta^\top Y_{t-1}$ is the deviation from equilibrium and $\alpha$ the speed at which each variable corrects it.