Dual-phase threshold selection methodology for modelling extreme events

Abstract

Extreme value theory is a method for modelling and evaluating risks in unusual or rare situations, and it has gained popularity in risk management. In general, the probability of extreme occurrences can be assessed by fitting a probability distribution to a sample of extreme observations. It is crucial to examine the tail shape of the distribution since it affects the estimation of parameters associated with extreme events. The extreme value index is a shape parameter that quantifies the tail behaviour of a distribution. Selecting an appropriate threshold is a major challenge in extreme value analysis, especially in peaks over threshold methods. The choice of threshold significantly impacts the bias-variance trade-off in extreme value models. The choice of the threshold based on the stability plot is often subjective. To address this challenge, we have developed an efficient dual-phase threshold selection method. This approach involves trimming non-exceedances through a two-phase procedure and using the Cramér-von Mises test to assess exceedances above a suitable threshold, thereby determining the optimal threshold. Exceedances above a certain threshold typically follow the generalized Pareto distribution asymptotically. Estimates of the return levels associated with their return periods can be used to predict the statistical properties (magnitude and frequency) of upcoming exceedances. A simulation study is conducted to evaluate the effectiveness of the proposed threshold selection method.