Paper: arXiv 2603.05260

Authors: Benjamin Köhler, Anton J. Heckens, Thomas Guhr

Abstract

Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value analysis for infinite correlated systems remains an open challenge, we propose a practical framework for handling a large but finite number of correlated time series. We develop our approach for finance as a concrete example but emphasize its generality. We study the extremal behavior of high-frequency stock returns after rotating them into the eigenbasis of the correlation matrix. This separates and extracts various collective effects, including information on the correlated market as a whole and on correlated sectoral behavior from idiosyncratic features, while allowing us to use univariate tools of extreme value analysis. This holds even for high-frequency data where discretization effects normally complicate analysis. We employ a peaks-over-threshold approach and thereby fully avoid the analysis of block maxima. We estimate the tail shape of the rotated returns while explicitly accounting for nonstationarity, a key feature in finance and many other complex systems. Our framework facilitates tail risk estimation relative to larger trends and intraday seasonalities at both market and sectoral levels.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative framework combining correlation matrix eigen-rotation with peaks-over-threshold univariate EVT to handle high-frequency multivariate time series. It effectively balances clear mathematical formulations of extreme value theory with high-frequency empirical backtesting on NYSE intraday data while explicitly addressing nonstationarity.

Research Flowchart

  flowchart TD
    A["<b>Research Goal:</b><br>Quantify tail risk in finite, multivariate,<br>and correlated high-frequency systems"] --> B["<b>Input Data:</b><br>High-frequency stock returns<br><i>(Nonstationary & Discretized)</i>"]
    
    B --> C["<b>Eigenbasis Rotation:</b><br>Rotate returns using correlation matrix<br>to decouple market, sector & idiosyncratic noise"]
    
    C --> D["<b>Peaks-Over-Threshold (POT):</b><br>Apply univariate EVT to rotated series,<br>accounting for nonstationarity & seasonality"]
    
    D --> E["<b>Tail Shape Estimation:</b><br>Model generalized Pareto distributions<br>on decoupled components"]
    
    E --> F["<b>Key Outcomes:</b><br>Accurate market & sector tail risk bounds<br>without block-maxima limitations"]

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0 of 57 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.