Testing for changes in (extreme) VaR

Abstract

In this paper, we develop tests for a change in an unconditional small quantile (Value-at-Risk, VaR, in financial time series analysis) based on an estimator motivated by extreme value theory. This so-called Weissman estimator allows tests to be applied for extreme VaR, where extant tests mostly fail. In view of applications, we allow for weakly dependent observations. Our test statistics rely on self-normalization, which obviates the need to estimate the complicated asymptotic variance. Consistency is shown under local alternatives, where multiple breaks can occur. A simulation study shows that in finite samples our tests compare favourably in the tail region with extant tests based on order statistic estimators and also with tail index break tests. Two empirical examples serve to illustrate the practical use of our tests.