Title: Loss function-based structural break detection in risk measures
Authors: Emese Lazar - University of Reading (United Kingdom)
Shixuan Wang - University of Reading (United Kingdom)
Xiaohan Xue - ICMA Centre, University of Reading (United Kingdom) [presenting]
Abstract: A new test is proposed to detect change points in risk measures, based on the CUSUM procedure applied to the Wilcoxon statistics of the FZ loss function class. This efficiently captures structural breaks jointly in two risk measure series: Value-at-Risk (VaR) and Expected Shortfall (ES). We derive the asymptotic distribution of the proposed statistic. Due to the existence of nuisance parameters, we adopt a stationary bootstrapping technique to obtain the critical values of the test statistics of the loss-based Wilcoxon test. Monte Carlo simulation results justify that our proposed test has better size control and higher power than the alternative tests under various change-point scenarios. The alternatives considered include structural break detection methods based on self-normalized CUSUM statistics for the VaR series and the ES series taken individually and a modification of our proposed statistic based on Renyi-type formulation. An empirical study of the S\&P 500 index illustrates that the proposed test is able to detect structural breaks in the tail of financial time series which are consistent with known market events.