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}
}