带约束系数平稳自回归过程的相合性结果
Consistency Results for Stationary Autoregressive Processes with Constrained Coefficients
摘要：
我们考虑系数限制在椭球内的平稳自回归过程，其中包括系数绝对可和的自回归过程。我们提供了一致性的结果，在不同的规范，这些过程的估计使用约束和惩罚估计。作为一个应用，我们证明了一些弱形式的普遍一致性。仿真结果表明，直接包括约束的估计可以导致更强大的结果。
英文摘要：
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.
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