Factorized Tail Volatility Model: Augmenting Excess-over-Threshold Method for High-Dimensional Hevay-Tailed Data

TL;DR

This paper introduces the FTVM-EoT framework, combining factorized tail volatility modeling with excess-over-threshold methods to analyze high-dimensional heavy-tailed data, improving tail risk estimation across quantiles.

Contribution

The paper develops the FTVM-EoT method, integrating high-dimensional tail volatility modeling with quantile thresholding, and provides an iterative estimation algorithm with asymptotic analysis.

Findings

FTVM-EoT outperforms existing methods at intermediate and extreme quantiles.

The framework effectively models tail risk in high-dimensional heavy-tailed data.

Simulation studies validate the robustness and accuracy of the proposed method.

Abstract

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.