Detecting Spurious Factor Models

Abstract

Spurious factor behaviors arise in large random matrices with high-rank signal components and heavy-tailed spectral distributions. This paper establishes analytical probabilistic limits and distribution theory of these spurious behaviors for high-dimensional non-stationary integrated systems, and stationary systems with near-unit-root spatial processes across cross sections. We transform scree plots into Hill plots to detect spectral patterns in these spurious factor models and develop multiple $t$-tests to distinguish between spurious and genuine factor models. Numerical analysis indicates that the existing spurious factor models fit some, but not all, economic datasets. In particular, the term structure of interest rates adheres to genuine factor models rather than the local correlation model.

Keywords: Factor models, random matrices, principal components, eigenvalues, central limit theorem, heavy tail, integrated time series, local correlation

JEL Classification: C01, C12, C23, C55,