Factorized Tail Volatility Model: Augmenting Excess-over-Threshold Method for High-Dimensional Hevay-Tailed Data
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866910979692953600 |
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| author | Hu, Yifan Hou, Yanxi |
| author_facet | Hu, Yifan Hou, Yanxi |
| contents | Ecess-over-Threshold method is a crucial technique in extreme value analysis, which approximately models larger observations over a threshold using a Generalized Pareto Distribution. This paper presents a comprehensive framework for analyzing tail risk in high-dimensional data by introducing the Factorized Tail Volatility Model (FTVM) and integrating it with central quantile models through the EoT method. This integrated framework is termed the FTVM-EoT method. In this framework, a quantile-related high-dimensional data model is employed to select an appropriate threshold at the central quantile for the EoT method, while the FTVM captures heteroscedastic tail volatility by decomposing tail quantiles into a low-rank linear factor structure and a heavy-tailed idiosyncratic component. The FTVM-EoT method is highly flexible, allowing for the joint modeling of central, intermediate, and extreme quantiles of high-dimensional data, thereby providing a holistic approach to tail risk analysis. In addition, we develop an iterative estimation algorithm for the FTVM-EoT method and establish the asymptotic properties of the estimators for latent factors, loadings, intermediate quantiles, and extreme quantiles. A validation procedure is introduced, and an information criterion is proposed for optimal factor selection. Simulation studies demonstrate that the FTVM-EoT method consistently outperforms existing methods at intermediate and extreme quantiles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00840 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Factorized Tail Volatility Model: Augmenting Excess-over-Threshold Method for High-Dimensional Hevay-Tailed Data Hu, Yifan Hou, Yanxi Methodology Ecess-over-Threshold method is a crucial technique in extreme value analysis, which approximately models larger observations over a threshold using a Generalized Pareto Distribution. This paper presents a comprehensive framework for analyzing tail risk in high-dimensional data by introducing the Factorized Tail Volatility Model (FTVM) and integrating it with central quantile models through the EoT method. This integrated framework is termed the FTVM-EoT method. In this framework, a quantile-related high-dimensional data model is employed to select an appropriate threshold at the central quantile for the EoT method, while the FTVM captures heteroscedastic tail volatility by decomposing tail quantiles into a low-rank linear factor structure and a heavy-tailed idiosyncratic component. The FTVM-EoT method is highly flexible, allowing for the joint modeling of central, intermediate, and extreme quantiles of high-dimensional data, thereby providing a holistic approach to tail risk analysis. In addition, we develop an iterative estimation algorithm for the FTVM-EoT method and establish the asymptotic properties of the estimators for latent factors, loadings, intermediate quantiles, and extreme quantiles. A validation procedure is introduced, and an information criterion is proposed for optimal factor selection. Simulation studies demonstrate that the FTVM-EoT method consistently outperforms existing methods at intermediate and extreme quantiles. |
| title | Factorized Tail Volatility Model: Augmenting Excess-over-Threshold Method for High-Dimensional Hevay-Tailed Data |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.00840 |