This paper investigates the structural changes in the parameters of first-order autoregressive models by analyzing the edge eigenvalues of the precision matrices. Specifically, edge eigenvalues in the precision matrix are observed if and only if there is a structural change in the autoregressive coefficients. We demonstrate that these edge eigenvalues correspond to the zeros of some determinantal equation. Additionally, we propose a consistent estimator for detecting outliers within the panel time series framework, supported by numerical experiments.

翻译：本文通过分析精度矩阵的边缘特征值，研究一阶自回归模型参数的结构变化。具体而言，当且仅当自回归系数存在结构变化时，精度矩阵中才会出现边缘特征值。我们证明这些边缘特征值对应于某个行列式方程的根。此外，我们提出一个一致估计量，用于在面板时间序列框架中检测异常值，并通过数值实验验证其有效性。