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

TL;DR

This paper studies how edge eigenvalues of precision matrices reveal structural changes in nonstationary autoregressive processes and introduces a consistent estimator for outlier detection.

Contribution

It establishes a link between edge eigenvalues and structural changes, and proposes a new estimator for outlier detection in panel time series.

Findings

Edge eigenvalues indicate structural changes in AR models.

Edge eigenvalues correspond to zeros of a determinantal equation.

Proposed estimator effectively detects outliers.

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.