Detecting structural breaks in tail behaviour -- from the perspective of fitting the generalized Pareto distribution

Abstract

Extreme Value Theory (EVT) is heavily applied in modelling tail behaviour. Previous literature uses the tail index to test for Structural Breaks (SBs) in the tails. This study presents another more reliable approach and relies on the outperformance of the Generalized Pareto Distribution (GPD) in modelling tails. The transformed GPD is treated as a classical Ordinary Least Square (OLS) regression and the generalized M-fluctuation test (Zeileis, 2005, 2006) is applied because it is a unified approach based on Maximum Likelihood (ML) scores (Andrews and Ploberger, 1994), <italic>F</italic>-statistics (1989, 1992), and OLS residuals (Ploberger and Kramer, 1992). The outcomes indicate that there are multiple SBs not only in all of the three exchange return series considered (UK Pound, Japanese Yen and New Taiwan Dollar, all versus US Dollar) but also GPD parameter estimation at extreme quantile levels. Based on these empirical analyses, it is advisable that EVT should be used with caution at extreme quantile levels.