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

Jiang Hu, Jiahui Xie, Yangchun Zhang and Wang Zhou

Papers from arXiv.org

Abstract: Factor models are essential tools for analyzing high-dimensional data, particularly in economics and finance. However, 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 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. We show that under magnifying perturbations, the eigenvalues associated with real factors exhibit significantly less fluctuation (stabilizing asymptotically) compared to spurious eigenvalues arising from heavy-tailed effects. This differential behavior allows the identification and detection of the true and spurious factors. 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 compared to existing methods, particularly in scenarios with pronounced heavy-tailedness.

Date: 2025-06
New Economics Papers: this item is included in nep-ecm and nep-ets
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