Consistency Results for Stationary Autoregressive Processes with Constrained Coefficients
This work addresses estimation challenges for constrained autoregressive processes, offering incremental improvements in robustness for statistical modeling applications.
The authors tackled the problem of estimating stationary autoregressive processes with coefficients constrained to an ellipsoid, providing consistency results under various norms and demonstrating that constrained estimation yields more robust outcomes in simulations.
We consider stationary autoregressive processes with coefficients restricted to an ellipsoid, which includes 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 some weak form of universal consistency. Simulations show that directly including the constraint in the estimation can lead to more robust results.