Optimal threshold determination based on the meanexcess plot

Abstract

Choosing a suitable threshold has been an issue in practice. Based on the mean excess plot (MEP), the eyeball inspection approach(EIA) is mainly used to determine the threshold. This involves fitting the threshold at the point the plot becomes approximately linear solely using one’s sense of judgement in such a way that Generalized Pareto model is valid. This is a rather subjective choice.In this paper, we propose an alternative way of selecting the thresh-old where, instead of choosing individual thresholds in isolation and testing their fit, we make use of the bootstrap aggregate of these individual thresholds which are formulated in terms of quantiles.The method incorporates the visual technique and is aimed at reducing the subjectivity associated with solely using the EIA. The new approach is implemented using simulated datasets drawn from three different distributions. An application to the NSE All share Nigerian stock index is presented. The performance of the proposed modeland the EIA are judged based on standard error, Negative log likeli-hood, the Akaike Information Criteria and the Bayesian Information Criteria. The results show that the new technique gives similar esti-mates as the EIA and in some cases it performs better. In compari-son to other existing methods, the proposed model performs well.