Tests for principal eigenvalues and eigenvectors

TL;DR

This paper develops statistical tests for principal eigenvalues and eigenvectors in large factor models, enabling detection of structural breaks and distinguishing their sources, with applications to financial data analysis.

Contribution

It introduces new two-sample tests for principal eigenvalues and eigenvectors in large factor models, enhancing structural break detection capabilities.

Findings

Tests successfully detect structural breaks in financial data

Methods distinguish between changes in eigenvalues and eigenvectors

Application to S&P 500 data demonstrates practical utility

Abstract

We establish central limit theorems for principal eigenvalues and eigenvectors under a large factor model setting, and develop two-sample tests of both principal eigenvalues and principal eigenvectors. One important application is to detect structural breaks in large factor models. Compared with existing methods for detecting structural breaks, our tests provide unique insights into the source of structural breaks because they can distinguish between individual principal eigenvalues and/or eigenvectors. We demonstrate the application by comparing the principal eigenvalues and principal eigenvectors of S\&P500 Index constituents' daily returns over different years.