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

TL;DR

This paper introduces a new method to accurately determine the number of true factors in heavy-tailed elliptical factor models by distinguishing genuine signals from noise-induced spurious eigenvalues through a fluctuation magnification technique.

Contribution

It proposes a novel fluctuation magnification algorithm and formal testing procedure to differentiate real factors from spurious ones caused by heavy tails in elliptical factor models.

Findings

The method effectively identifies true factors in heavy-tailed data.

Simulation studies show improved accuracy over existing methods.

Real data analysis confirms practical applicability.

Abstract

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.