Change-Point Testing for Risk Measures in Time Series

TL;DR

This paper introduces new change-point testing methods for nonparametric risk measure estimators in time series, enabling detection of multiple tail distribution changes without standard error estimation, supported by theoretical and empirical evidence.

Contribution

It develops self-normalized change-point tests for risk measures in dependent time series, with theoretical guarantees and practical application to financial data.

Findings

Effective detection of tail distribution changes in financial data

Theoretical validation via functional central limit theorems

Empirical demonstration on S&P 500 and US Treasury bonds

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 instability in the tails of financial time series.