Search for: [Abstrakt = "The authors discuss the estimation of a change\-point ??0 at which the parameter of a \(non\-stationary\) AR\(1\)\-process possibly changes in a gradual way. Making use of the observations ??1, … , ???? , we study the least squares estimator ??̂0 for ??0, which is obtained by minimizing the sum of squares of the residuals with respect to the given parameters. As the first result it can be shown that, under certain regularity and moment assumptions, ??̂0\/?? is a consistent estimator for ??0, where ??0 = ⌊????0⌋, with 0 < ??0 < 1, i.e., ??̂0\/?? →?? ??0 \(?? → ∞\). Based on the rates obtained in the proof of the consistency result, a rough convergence rate statement can also be given. Some possible further investigations are briefly discussed, including the weak limiting behaviour of the \(suitably normalized\) estimator."]

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