stability of VAR model

The VAR model is stable if it generates Stationary time series - all of them. This is a little intense to think about since each variable can depend on lags of other variables.

A VAR(p) is stable if the (modulus of the) eigenvalues of the coefficient matrix are less than 1. This works even for p > 1 since we can make an augmented matrix holding all the other matrices which is equivalent

I & 0 & \cdots & 0 & 0 \\ 0 & I & \cdots & 0 & 0 \\ \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & \cdots & I & 0 \end{bmatrix} $$