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On the edge eigenvalues of the precision matrices of nonstationary autoregressive processes

Methodology 2026-01-14 v4 Statistics Theory Statistics Theory

Abstract

This paper investigates 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 show that these edge eigenvalues correspond to the zeros of a determinantal equation. Additionally, we propose a consistent estimator for detecting outliers within the panel time series framework, supported by numerical experiments.

Keywords

Cite

@article{arxiv.2109.02204,
  title  = {On the edge eigenvalues of the precision matrices of nonstationary autoregressive processes},
  author = {Junho Yang},
  journal= {arXiv preprint arXiv:2109.02204},
  year   = {2026}
}