The Spurious Factor Dilemma: Robust Inference in Heavy-Tailed Elliptical Factor Models

Standard methods for determining the number of factors often overestimate the true number when data exhibit heavy-tailed randomness, misinterpreting noise-induced outliers as genuine factors. This paper addresses this challenge within the framework of Elliptical Factor Models (EFM), which accommodate both heavy tails and potential non-linear dependencies common in real-world data. We demonstrate, both theoretically and empirically, that heavy-tailed noise generates spurious eigenvalues that mimic true factor signals. To distinguish these, we propose a novel methodology based on a fluctuation magnification algorithm. Under mild conditions, we show that, by magnifying perturbations, the eigenvalues associated with real factors exhibit significantly less fluctuation (stabilizing asymptotically) than spurious eigenvalues arising from heavy-tailed effects. We develop a formal testing procedure based on this principle and apply it to the problem of accurately selecting the number of common factors in heavy-tailed EFMs. Simulation studies and real data analysis confirm the effectiveness of our approach, particularly in scenarios with pronounced heavy-tailedness.