Hi prof. Pfeifer, may I ask this question.

If model1 has higher persistence (measured by the modulus of its largest eigenvalue) relative to model2, it does not necessarily mean all IRFs of model1 will be more persistent than that of model2, right?

I simulated the general solution of some dynamic system with two different set of eigenvalues. And indeed, the model with the largest eigenvalue in absolute terms (model1) is more persistent. But these are not IRFs.

I built two different VAR models (second figure attached) for two sectors. Only data changes, but same model.

Modulus of the largest eigenvalue of the model with BLUE IRFs is 0.809.

Modulus of the largest eigenvalue of the model with BROWN IRFs is 0.708.

I was kinda expecting BLUE IRFs to be relatively more persistent for all shocks in the model. But that appears not to be the case.

Many thanks for you comment!!

SIMULATED DYNAMIC MODEL

model 1: \lambda (eigenvalues) = 0.8, 0.4

[x_t, y_t]' = 0.8^t [2, 1]' + 0.4^t [1, -1]'

model 2: \lambda(eigenvalues) =0.7, 0.6

[x_t, y_t]' = 0.7^t [2, 1]' + 0.6^t [1, -1]'

VAR model