Asymptotic properties of estimators for autoregressive models with errors in variables

Let {Xt, t ∈ ℤ} be an observable strictly stationary sequence of random variables and let Xt = Ut + εt, where {Ut} is an AR (p) and {εt} is a strictly stationary sequence representing errors of measurement in {Xt}, with Ε{ε1} = 0. Under some broad assumptions on {εt} 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.