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.

翻译：标准因子数量确定方法在处理具有重尾随机性的数据时，常会高估真实因子数量，将噪声引发的异常值误判为真实因子。本文在椭圆因子模型框架下应对这一挑战，该模型能够同时容纳现实数据中常见的重尾特征与潜在非线性依赖关系。我们从理论与实证两方面证明，重尾噪声会产生与真实因子信号相似的伪特征值。为区分二者，我们提出一种基于波动放大算法的新方法。在温和条件下，我们证明通过放大扰动，真实因子对应的特征值相较于重尾效应产生的伪特征值表现出显著更小的波动性（渐近稳定）。基于此原理，我们构建了形式化的检验程序，并将其应用于重尾椭圆因子模型中公共因子数量的准确选择问题。模拟研究与实际数据分析证实了本方法的有效性，尤其在重尾特征显著的情境中。