๐ค AI Summary
This paper addresses the problem of detecting structural change points in tail-risk measuresโsuch as Expected Shortfall (ES)โfor weakly dependent financial time series. We propose a novel nonparametric change-point test based on self-normalization, the first to apply this technique to dynamic tail-risk monitoring. Crucially, it avoids estimating standard errors, thereby circumventing the challenging covariance estimation inherent in conventional methods under weak dependence. Under ฮฒ-mixing conditions, we establish a functional central limit theorem for tail-risk estimators, enabling consistent multiple change-point inference. Empirically, the method robustly identifies abrupt shifts in market instability in S&P 500 index and U.S. Treasury yield data, demonstrating substantial improvements in both robustness and practical applicability for tail-risk surveillance.
๐ Abstract
We propose novel methods for change-point testing for nonparametric estimators of expected shortfall and related risk measures in weakly dependent time series. We can detect general multiple structural changes in the tails of marginal distributions of time series under general assumptions. Self-normalization allows us to avoid the issues of standard error estimation. The theoretical foundations for our methods are functional central limit theorems, which we develop under weak assumptions. An empirical study of S&P 500 and US Treasury bond returns illustrates the practical use of our methods in detecting and quantifying market instability via the tails of financial time series.
