Change-Point Testing for Risk Measures in Time Series

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.

Keywords: Time Series, Risk Measure, Change-Point Test, Confidence Interval, Self-Normalization, Sectioning, Expected Shortfall, Unsupervised Change Point Detection

JEL Classification: C14, C58, G32