## Controlling for stationarity when simulating a VAR(p)-model

I am interested in simulating a bunch of VAR(p) models, i.e. I want to simulate the model parameters, and then simulate a time series from that model. This I would like to do many times. However, one of the restrictions that I have, is that the simulated VAR(p) models must be covariance-stationary.

My idea right now is as follows: A VAR(p) model can be rewritten as a VAR(1) model; $\mathbf{Y}_t = \mathbf{F}*\mathbf{Y}_{t-1} + \mathbf{v}_t$. And for this system to be stationary, the absolute values of the eigenvalues of the matrix $\mathbf{F}$ must be less than 1. I am thinking of simulating these eigenvalues, and then moving backwards to recreate the matrix $\mathbf{F}$. Does anyone know if this is a feasible solution? Any other/better way of doing this?

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