# A Finite-Sample Deviation Bound for Stable Autoregressive Processes

arXiv: https://arxiv.org/abs/1912.08103 · HTML: https://mlsanity.com/paper/1912.08103/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [SAMoSSA: Multivariate Singular Spectrum Analysis with Stochastic Autoregressive Noise](https://mlsanity.com/paper/2305.16491/) (2023)
- [ℓ1-Regularized Generalized Least Squares](https://mlsanity.com/paper/2405.10719/) (2024)

## Abstract (arXiv)

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 chi2 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.