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

Fuente: arXiv
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Main Authors: Hu, Jiang, Xie, Jiahui, Zhang, Yangchun, Zhou, Wang
Format: Preprint
Published: 2025
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author Hu, Jiang
Xie, Jiahui
Zhang, Yangchun
Zhou, Wang
author_facet Hu, Jiang
Xie, Jiahui
Zhang, Yangchun
Zhou, Wang
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_05116
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Spurious Factor Dilemma: Robust Inference in Heavy-Tailed Elliptical Factor Models
Hu, Jiang
Xie, Jiahui
Zhang, Yangchun
Zhou, Wang
Methodology
Econometrics
Statistics Theory
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.
title The Spurious Factor Dilemma: Robust Inference in Heavy-Tailed Elliptical Factor Models
topic Methodology
Econometrics
Statistics Theory
url https://arxiv.org/abs/2506.05116