How to impose restrictions on a parameter matrix

Suppose you want to estimate a VAR(1) model and you declare the matrix X (independent variable) and Y (dependent variable).

Estimating a VAR model can then be done via OLS, so b=(X'X)\X'Y. However, how can you impose restrictions such that the eigenvalues of this b matrix are between -1 and 1.

This way the VAR model is stable.

Answer 1

[Hang Qian]

Hi Imner,

Eigenvalue restrictions are nonlinear constraints imposed on the least square estimators. To estimate parameters, we may consider functions like FMINCON which supports nonlinear constraints. However, if some constraints are binding, inference might be challenging.

Bayesian VAR is an alternative and we could impose parameter constraints with rejection sampling.