Consistency and asymptotic normality of least-squares estimators are discussed for the linear autoregressive model with explanatory variables. Few assumptions are made about the error sequence. The case of stochastic explanatory variables is also considered.
"On the Asymptotic Properties of Least-Squares Estimators in Autoregression." Ann. Statist. 8 (1) 132 - 146, January, 1980. https://doi.org/10.1214/aos/1176344896