Consistency Results for Stationary Autoregressive Processes With Constrained Coefficients

We consider stationary autoregressive processes with coefficients restricted to an ellipsoid. These are included in the family of autoregressive processes with absolutely summable coefficients. We provide consistency results under different norms for the estimation of such processes using constrained and penalized estimators. As an application, we show a weak form of universal consistency. Simulations show that directly including the constraint in the estimation can lead to results that are more robust.