Let ${X_t, t \epsilon \mathbb{Z}}$ be an observable strictly stationary sequence of random variables and let $X_t = U_t + \varepsilon_t$, where ${U_t}$ is an AR (p) and ${\varepsilon_t}$ is a strictly stationary sequence representing errors of measurement in ${X_t}$, with $E{\varepsilon_1} = 0$. Under some broad assumptions on ${\varepsilon_t}$ we establish the consistency properties as well as the rates of convergence for the standard estimators for the autoregressive parameters computed from a set of modified Yule-Walker equations.