  In this paper, we study finite-sample properties of the least squares
estimator in first order autoregressive processes. By leveraging a result from
decoupling theory, we derive upper bounds on the probability that the estimate
deviates by at least a positive $\varepsilon$ from its true value. Our results
consider both stable and unstable processes. Afterwards, we obtain
problem-dependent non-asymptotic bounds on the variance of this estimator,
valid for sample sizes greater than or equal to seven. Via simulations we
analyze the conservatism of our bounds, and show that they reliably capture the
true behavior of the quantities of interest.
