# Consistency Results for Stationary Autoregressive Processes with Constrained Coefficients

## TL;DR

This paper investigates the estimation consistency of stationary autoregressive processes with constrained coefficients, demonstrating theoretical results and practical benefits of including constraints directly in estimation.

## Contribution

It provides new consistency results for constrained and penalized estimators in autoregressive models with coefficients in an ellipsoid, including universal consistency and robustness insights.

## Key findings

- Constrained estimators improve robustness in autoregressive process estimation.
- Consistency results hold under various norms for these estimators.
- Simulations confirm practical advantages of direct constraint inclusion.

## Abstract

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.