VAR(2) model how to convert it to VEC(2) model

Question

I have the below VAR(2) model and I need to convert it into VEC representation how can I do it? Where can I find similar example or what is the way I should follow?

Answer 1

You can specify your VECM model as:

$$\Delta y_t = \Pi y_{t-1} + \theta \Delta y_{t-1} + u_t $$

where $\Pi = (A_1 + A_2) - I,$ and $ \theta = -A_2 $.

The number of lags in VECM is one less than in VAR. In general, any VAR(p) can be specified as VECM:

$$\Delta y_t = v + \Pi y_{t-1} + \sum_{i=1}^{p-1}\theta_i \Delta y_{t-i} + u_t $$

where $\Pi = \sum_{j=1}^p A_j - I $ and $ \theta_i = - \sum_{j=i+1}^p A_j $