标题： 虚假因子困境：重尾椭圆因子模型中的稳健推断 显示英文标题

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

摘要： 因子模型是分析高维数据的重要工具，尤其是在经济学和金融学领域。 然而，标准的确定因子数量的方法在数据表现出重尾随机性时，往往高估真实因子的数量，将由噪声引起的异常值误认为是真实的因子。 本文在椭圆因子模型（EFM）框架内解决了这一挑战，该模型能够同时处理现实数据中常见的重尾性和潜在非线性依赖性。 我们从理论上和实证上证明了重尾噪声会产生虚假的特征值，这些特征值会模拟真实的因子信号。 为了解决这个问题，我们提出了一种基于波动放大算法的新方法。 我们表明，在扰动放大的情况下，与真实因子相关的特征值相比，由重尾效应产生的虚假特征值表现出显著更大的波动（渐近趋于不稳定）。 这种差异行为使得我们可以识别和检测出真正的因子和虚假因子。 我们基于此原理开发了一种正式的检验程序，并将其应用于准确选择重尾EFM中公共因子数量的问题。 仿真研究和真实数据分析验证了我们的方法相对于现有方法的有效性，特别是在重尾性明显的场景下。 显示英文摘要

摘要： 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.