Malaysian Journal of Mathematical Sciences, September 2025, Vol. 19, No. 3
An Assessment on Threshold Selection for Generalized Pareto Distribution using Goodness of Fit
Alif, F. K., Ali, N., and Safari, M. A. M.
Corresponding Email: norhaslinda@upm.edu.my
Received date: 19 December 2024
Accepted date: 10 March 2025
Abstract:
In real-world datasets, particularly those related to finance and rainfall, the study of extreme values is essential for understanding the return levels of extreme events and assessing financial risks. Accurate analysis of these extremes can play a crucial role in disaster prevention and risk management. While the generalized Pareto distribution remains a widely used tool for extreme value modeling, its threshold selection method poses challenges, notably the subjectivity of the mean residual life plot. This research presents an automated, step-by-step threshold selection procedure that is computationally efficient and objective. The method evaluates interval-based candidate thresholds and employs goodness-of-fit tests to identify the optimal threshold, maximizing the $p$-value. Of the various combinations of estimation methods and goodness of fit tests assessed in this study, the Anderson Darling-L-moments and Cramer-von Mises-Lmoments combinations demonstrated superior performance. Simulation studies indicated that our approach offers notable performance improvements compared to widely recognized non-automated method and several existing automated procedures. The proposed method was applied to real-life datasets from both the rainfall and financial domains, confirming its robustness. Additionally, a bootstrap approach was used to quantify the uncertainty of the selected threshold and its impact on return level estimates.
Keywords: extreme values; generalized Pareto distribution; automated; threshold selection; return level; goodness of fit
