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

A Finite-Sample Deviation Bound for Stable Autoregressive Processes