Asymptotic properties of estimators for autoregressive models with errors in variables

The Annals of Statistics · 1996 · Volume 24 · Issue 1

Abstract

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.

Keywords

62F12; 62M10; Error in variable autoregressive model; identifiable parameter;

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