Consistency results for stationary autoregressive processes with constrained coefficients

Alessio Sancetta

doi:10.1109/TIT.2018.2870373

Consistency results for stationary autoregressive processes with constrained coefficients

Alessio Sancetta

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Abstract

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 more robust results.

Original language	English
Pages (from-to)	538 - 550
Number of pages	13
Journal	IEEE Transactions on Information Theory
Volume	65
Issue number	1
Early online date	19 Sept 2018
DOIs	https://doi.org/10.1109/TIT.2018.2870373
Publication status	E-pub ahead of print - 19 Sept 2018

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10.1109/TIT.2018.2870373

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Cite this

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abstract = "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 more robust results.",

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AB - 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 more robust results.

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