The Spurious Factor Dilemma: Robust Inference in Heavy-Tailed Elliptical Factor Models
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910038408298496 |
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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 |
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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 |