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

2025-06-05

AI Summary

Under heavy-tailed elliptical factor models (EFMs), conventional factor number selection methods systematically overestimate the true number of factors by misclassifying outliers—induced by heavy-tailed noise—as genuine factors. To address this, we propose a robust inference framework grounded in eigenvalue perturbation stability: genuine factors exhibit eigenvalues stable under perturbation, whereas spurious ones yield eigenvalues that amplify readily. Leveraging this contrast, we construct the first hypothesis-testing framework for factor number determination specifically tailored to heavy-tailed EFMs. Our approach integrates a volatility amplification algorithm, elliptical distribution theory, and asymptotic random matrix analysis. Extensive simulations and financial empirical studies demonstrate substantial improvements in estimation accuracy: in strongly heavy-tailed settings, our method reduces misclassification rates by over 40% compared to state-of-the-art alternatives.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Intelligent Robots: State Estimation
• Machine Learning: Ensemble Methods

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

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.

Problem

• Distinguish true factors from noise-induced outliers in heavy-tailed data
• Develop method to identify spurious eigenvalues in Elliptical Factor Models
• Accurately select number of common factors in heavy-tailed scenarios

Innovation

• Fluctuation magnification algorithm distinguishes factors
• Stable eigenvalues identify true factors
• Formal testing procedure for factor selection