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arXiv · 1912.08103

A Finite-Sample Deviation Bound for Stable Autoregressive Processes

Rodrigo A. González·Cristian R. Rojas
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Abstract

In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $\chi^2$ distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, we present a problem-dependent finite-time bound on the deviation probability of any fixed linear combination of the estimated parameters of the AR$(n)$ process. We discuss extensions and limitations of our approach.

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BibTeXRIS

Rodrigo A. González, Cristian R. Rojas. 2019-12-17. A Finite-Sample Deviation Bound for Stable Autoregressive Processes. https://arxiv.org/abs/1912.08103

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