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This paper investigates the structural change of the coefficients in theautoregressive process of order one by considering eigenvalues of an inverseToeplitz matrix. More precisely, under mild assumptions, extreme eigenvaluesare observed when the structural change has occurred. A consistent estimator ofextreme eigenvalues is provided under the panel time series framework. Theproposed estimation method is demonstrated with simulations.

On the extreme eigenvalues of the precision matrix of the nonstationary  autoregressive process and its applications to outlier estimation of panel  time series