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

This paper investigates the structural change of the coefficients in the autoregressive process of order one by considering eigenvalues of an inverse Toeplitz matrix. More precisely, under mild assumptions, extreme eigenvalues are observed when the structural change has occurred. A consistent estimator of extreme eigenvalues is provided under the panel time series framework. The proposed estimation method is demonstrated with simulations. This estimation scheme can be used in a general structural change model such as an autoregressive model with heteroscedasticity.