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Asymptotic properties of estimators for autoregressive models with errors in variables. (English) Zbl 0853.62070

Summary: Let \(\{X_t, t \in \mathbb{Z}\}\) be an observable strictly stationary sequence of random variables and let \(X_t = U_t + \varepsilon_t\), where \(\{U_t\}\) is an \(\text{AR} (p)\) 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F12 Asymptotic properties of parametric estimators
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